Hi there friends and subscribers welcome back to my YouTube channel. This is Daniel Rosal here bringing you today's video From Jerusalem as per the usual I was going to bed last night and briefly took out my tablet to watch a bit of YouTube and on my home page There was this video released by the Israel Police in Hebrew Mesh-tarrat Yisra'el And they released basically interrogation footage that I thought was very very interesting of Hamas terrorists who were captured alive either on October 7th itself the day of the horrific massacre of civilians in Israel or perhaps Was the next day? It's not clear. It's also not clear whether this interrogation was conducted by Israel Police or by the Shin Bet, which is the Israeli internal security Organization the Shabbat in Hebrew doesn't really matter in any event the interrogation up there was basically in Hebrew in Arabic with Hebrew subs The interrogation is conducted in Arabic the interrogator is speaking Arabic the detainees are speaking Arabic And there was just loads of comments saying, you know Someone needs to add English subtitles because it's so important this this footage is so important to trying to understand The mindset of the people who committed these atrocities. So I logged on today to YouTube and I saw someone had Volunteered their efforts to add the English subs that person's called Elan Sherman So just to be clear from copyright this footage was released by Israel Police The subtitles were added by Elan Sherman and I'm here to just add a little bit of commentary To this footage myself. So that's basically all I'm doing here I don't want to call this a reaction vid Because I think those reaction videos are super cheesy But I thought I'd just drop in with a few comments here and there as I play back this tape Just to add a little bit of context. So I'm gonna pop on my headphones now and Let's go and watch this video from the top. So let's just jump over to the screen here So these guys you're gonna be seeing are the the guys sitting here are the Hamas people and the guy off-camera Is the interrogator and presumably this was done in something like an Israeli police station. I don't know Alright, let's play Hamada So first comment here just to point out that the way they is really police released and structured this videotape is they do it section by section of the interrogation from each detainee and at the start of the opening clip what we're seeing is them trying to just establish the particulars what's your name and which organization do you work from in Hamas. So this guy said he worked for Al-Qassam which is basically the Al-Qassam brigade is the paramilitary wing of Hamas. Hamas also has a kind of political wing and the Al-Qassam brigade specifically is the organization which carried out the barbaric massacre on October 7th. You're going to see just in a second the guy ask whether they belong to Al-Qassam or Al-Nukba. Al-Nukba is more like an elite special forces organization within the Hamas. So the point of this really is they're trying to understand the chain of command and who each of these people belong to and who their commanders are because those are people that have been probably already killed or are on the kill list for Israel. It's possible of course that the captives know that this footage is going to be released so they're trying to make themselves sound better because it wasn't there is there you know there's been clear evidence that these guys raped women so you know what this guy is saying perhaps this really was the order he his team was given that what it was to basically spare just capture capture the women and children and just basically mow down the men but that's not actually what transpired so I just wanted to make note of that. So that's again just pretty pretty revealing that from the perspective of these jihadists and radical elements you know the guy asked him were the instructions specifically to co-civilians or army people and he said it doesn't really matter that's not a that's not a difference we were sweating over because for these guys from their worldview all Israeli citizens are legitimate military targets that's their worldview they want to liberate all of Israel from the Jews and whether the the Jew has served in an IDF position was a conscript is a conscript does not matter to them I think that's very clear also something else I just wanted to point out or drop in with an observation is when these guys were captured or in Israel some intelligence with gathered about their preparedness and it turns out they were very well prepared for this they were training for this operation for about two years they had very detailed information regarding the actual layout of the kibbutzim we're going to hear mentioned and they had very detailed information about the IDF that was basically obtained from reconnaissance so you're seeing a bit of this as this video clip goes on that these guys were well prepared for for what they did I think what interesting thing here is that from these guys the kind of killing seems to be just like an afterthought they're so um unquestioning of the idea that they would just mow down civilians that you know their their orders were to conquer this kibbutz and the guys asking well what does that mean to conquer you just want to live there like what about the people in the houses and it's just kind of like an afterthought for these guys oh yeah we just like we're just just kill those people um very disturbing and hey and it's none of them seem to have um very much in the way of remorse in another weird word they're using here is cleanse you see this uh sort of discourse in the jihadi palestinian extremism a lot to cleanse the land of jews and again that specific word cleansing is just to understand basically ethnic cleansing right that's what they were doing um I think that's important revealing as well okay this is super super important so um each captured for each captured civilian these guys were being compensated with ten thousand dollars in cash and an apartment you have to remember and understand that gaza or as it's pronounced in arabic gaza is a impoverished territory and ten thousand dollars and a house is huge so um again these guys are just saying well that's kind of the arrangement we had so basically they were incentivized now there's about more than 220 the last time I checked Israeli prisoners in gaza um so you know that's basically you're kind of trying to understand the motive of these guys it's a coming it'll sort of get clear in the video it's a coming out of islamic extremism or is it coming out of simple desperation about their life in gaza and you know these guys might be barely able to afford food and these strong men from Hamas come and tell them we're doing this operation capture capture in israeli ten thousand bucks if you take ten hostages back to gaza uh you get yourself an apartment and a hundred k in spending money so that creates a very powerful incentive for people who may be in poverty I'm not I'm not justifying at all at the disgusting actions of them but I just just pointing out that their motives are uh they're ascertaining their motives at this point in the interrogation this guy is uh one of this particular detainee is interesting it seems to be in a lot of emotional distress this guy here um I think what's interesting is that Israel Israel's police Israel police's decision to um publish this interrogation basically puts these guys in a terrible position I think these guys would be dead men if they return to gaza or um any arab country these guys would be hunted down as uh you know for betraying Hamas by revealing even these little morsels of information to the israelis or to or to the jews as the Hamas tend to refer to us so you know in the event of a prisoner exchange in which Israel receives hostages for Hamas people uh these guys if they were included in that exchange Hamas won't be asking for them the only reason Hamas would be asking for them is because they're going to put a bullet in their head so uh these guys are I think talking not uh because they've been tortured there doesn't seem doesn't seem to be what's happening these guys are up shits creek excuse my language they're either going to rot away for the rest of their lives in an Israeli jail or they're going to be released and killed by Hamas so um that would make you pretty distressed I can imagine uh just to point out for all the people who say that Hamas doesn't use human shields this is a Israeli propaganda uh we just had a guy admitting to doing exactly that during their operation not that I think there's any doubt for reasonable people that this happens but this guy um is wearing a t-shirt just to point out the obvious that appears to be covered in blood uh so whether again this interrogation was conducted immediately or the next day and he hasn't had a chance to change his clothes but uh that looks like dried blood on his shirts so they're just referring to uh just to fill in one one small bit of context Barry is one of the kibbutzim around the Gaza Strip so there was so all these names are just referring to different kibbutzim that are just right on the edge of the Gaza Strip where these guys infiltrated and committed the massacre so remember again just the nukhba is basically the kind of an elite more elite fighting force aqa sambar gate within Hamas is a bigger paramilitary group and the nukhba are kind of the elites if you will within their organization so just again just to reemphasize this operation took two years to plan and these guys were firstly drugged drugged up that's just sort of an important detail they were on a drug called fentanyl i think not fentanyl theophiline and amphetamine basically you know high as kites when they were doing this i don't know these guys particularly but a lot of the Hamas fighters were found dead with supplies of these pills but so they were kind of high as they were committing this and they came really well prepared with all this different gear that this guy's talking about like the bar in the detonation charges and then you how to use it so this wasn't really just a case of kind of these crazy isis like characters coming with firing off randomly rounds and rounds and rounds from you know from machine guns these guys actually came with a whole kind of kit in order to kill as many civilians as possible and take them captive into a raza He was in charge of the strike He was in charge of the strike Mohammad was in charge of the strike You were the only one What did you do? Mohammad was in charge of the strike Who was in charge of the strike? 40 to 40 years ago What did he do? He was a water purifier Was he with him in the strike? No He was surprised Why? So again, just little insights here into what this was like They basically caught the village by surprise This was about the assault started at 6.30 in the morning So early Saturday morning On a Jewish holiday day Some hat Torah here in Israel And as they say They encountered people watering their plants Taking their dogs for a walk Just mundane activities in these little agricultural villages To just happen to be on the outskirts of the Gaza Strip What was the need to use the plants for the villagers?  I don't know Each of them had 10 dogs Each of them had 2-3 dogs Were they armed with weapons? No, they didn't It was like that It was like that Is this in the Qur'an? No According to the Qur'an Is this in the Qur'an? Is this in the Qur'an?  There's no difference There's no evidence According to Islam Is this how people kill children? No, not from Islam What is Islam? Is Islam accepted? No, it's not It's not a 10-year-old So there are 8 people in the world who did what you did? There are 10 people It's clear that you kill people What's the difference between this work and Islam? It's clear that you kill people What?  You, Hamas If you're in the neighborhood and you're saying that you kill people Do you think like that? No, I don't I live in Qatar or Turkey And I speak in the name of the Muslims And I'm saying that I kill people Again, this is very, very interesting that these... I don't want to say they feel a sense of shame Because I feel like that's giving these guys too much credit But they do feel, to an extent This is kind of the first self-awareness we've seen in the video They seem angry that they've been used as pawns by the Hamas Leaders who are in, as they say, sitting in comfort in Turkey And they used this term, they left us on the outside Or on the inside, meaning in Israel And they're on the outside in these kind of safe other countries Who are the leaders of these Hamas? We listen to them, Haniyah Khaled Mashal So they think that they're laughing at you? No, they're laughing at us They're laughing at us, they're laughing at us They're laughing at us The leader of our tribe Who? People? Who do you call Hamas? Hamas, all of them Who is Hamas? Sunmar, Haniyah Abu Khaled Ramadan al-Rus What do you call them? Dambar al-Ghazl Why Dambar al-Ghazl? All of these things, you see, in Dail Ghazla Dail Ghazla Dammati al-Ghazl Who is Dambar al-Ghazl? Who is Dambar al-Ghazl? Thanks for watching this video guys and if you do want to get more videos from me regarding the situation here in Israel and more generally life in Israel then please do consider subscribing as I always say at the end of my videos to this YouTube channel Thank you for watching


Tako, počekaj sem počekal, da je F2M, kaj je zelo. Tako, imamo Fn, neč negativne, neč negativne, in imamo, da Fn konversuje v F, nekaj nekaj, The last time, we prove that the integral of the point-wise limit is less than or equalum than the limit of the designer'smax infinity is equal to term for the integral of e over听. OK. Now we will see some example, for instance, concerning the fact that here less or equal is really needed. I mean, you cannot put just an equal. So let's see this example. So do you have in mind something, for instance? Can you provide an example of some function, easy one, of some function, of a sequence of function fn, which converts point wise to some function f, but such that this inequality holds with the strict sign. It's always usually the same example, which, OK. One, I mean, there are many, of course, but one of these, yeah. Yeah, exactly. Yeah, OK. For instance, if you take e equal to the all real line, and fn of x equals to the characteristic function of this interval, OK. Then, of course, we have that fn of x, OK, fn converts to f, OK, converts to f, which is equal to 0, almost everywhere in r. But this is equal to 1 for any n, and this is equal to 0. So, of course, you have that, in this case, inequality also with the strict sign, with the strict less. OK, the limit, of course, is 1, so it's less than. OK, then, OK, the limit, of course, in this case, you can write here the limit, no, because the limit exists. But it might be also some example on which the limit does not exist, the limit of the integral of the fn, OK. In this case, it exists, you have the strict sign, but here you can replace the limit with the limit. So, let's see another example. Consider e again is the whole real line, and you define fn of x in this way is equal to 2 plus minus 1 n of key n n plus 1 of x. OK, so basically, you have that fn of x is equal to, 3 of key plus 1, if n is even, and it is equal to just key n out. OK, so in that case, you immediately see that if you take the integral here, OK, of course, the values of the integral depends on which kind of integer are you considering, OK. So you have that, again, fn converts to f to 0, almost everywhere in r, OK, but in this case fn, the integral, you know, does not converge, so does not converge. So you have two different limits, OK, so you have, so the limit in this case of the fn is 1, OK. So this is somehow an example for which you have the strict inequality, and you really need to put here the limit, OK, because the limit does not exist. OK, OK, and then I will give you still another example, but in a bounded domain, OK, here we take e to be equal to 0, 1. So the case, now consider the case where the measure of e is bounded. OK, so just let me define the function, a sequence of function fk by their graph, I mean, it's very, it's clear how you can, if you want to write an analytical definition, but OK. So it's, for instance, it's equal to 1, here, or not, equal to k, actually, and equal to 1 over k, OK, and then they are 0, assume that here is 1, so the graph looks like some, this triangle, OK. So basically the area is always 1, OK. So also in this case you have that fk converges to 0, almost everywhere in 0, 1, OK, because however you fix some point x, then you will find an integer that step out of x, OK. So you are in the domain where fk is, if k is sufficiently large, you are in the domain where fk has value 0. OK, and so you have 0, 1, 0, sorry, the integral of 0, 1 over k is equal to, yeah, yeah, the area here is 1 over 2, I'm sorry, before I said 1 is 1 over 2, 1 over 2, but I mean, it's constant, and OK, so in this case, also in this case you have that the integral of 0 is less, strictly less than the limit, plus infinity of 0, 1. Is that a triangle, OK? So you have, this is the area. This is 1 divided by k. 1 divided by k. You just apply the area, OK. And, OK. OK, now we will somehow provide the other result of convergence under the sign of integral using the Fatouzlem, OK. May I erase this? Sorry, the point was limit. I mean, this is a convergence actually everywhere. I wrote almost everywhere, because it's enough, but it's, no, I didn't get your question. I mean, when k, you're not convinced that this is the limit, because basically the idea is the following now, is that, so you fix, we are talking about point-wise convergence, so you fix one x, even if it's here, you know that if you take k sufficiently large, this would look like something like this, OK. If k is sufficiently large, then the graph of fk would look like this. So this x, the x that you fix, will fall in the part of the domain of the fk, where fk is 0, OK. And then, OK. And this is, OK. OK, now, in state, these are other theorem, the monotone convergence theorem, which is also known under the name of Beppolevi theorem, OK. It's monotone convergence, Beppolevi theorem, which is an Italian mathematician. OK, of course, by the name, you understand that we need to put some requirement on the monotonicity of our function, of our sequence fn, OK. So we start by fn be an increasing sequence in measurable function, OK. Of non-negative, because so far we know how to come to this non-negative measurable function, OK. And let f be the point-wise limit fn, then we have that really, the integral of f can be computed as the limit of the integral of fn. Something we gain more with respect to the Fattulema, because here we have the equality, OK, and we have the limit, but of course we also require more, OK, because we have this monotonicity requirement, OK. OK, from one side we use the Fattulema, so by the Fattulema we are under the hypothesis of the Fattulema, we have that this is less or equal than the limit and then we need to prove the other way around, OK. OK, now of course we have to use our hypothesis, our monotonicity hypothesis. OK, so let fn is an increasing sequence, so we have that, OK, since increasing sequence, OK, then we have that fn is less or equal to less than fn plus one and for what we prove fn will be which is convergence to F, so we have this, OK. It's an increasing sequence, so the inequality is preserved to the limit. OK, so just take the little soup, the lim soup on the left hand side and so we have that the lim soup as n tends to plus infinity of n is larger or equal than the F, OK. So if you combine these two you obtain that the t is just by observing that of course the lim soup is larger or equal, but in general it's larger or equal than the lim soup, OK. So you get that. OK, now we see some corollary of this monotonic convergence theorem. So now we consider u n a sequence, so again it's u n b a sequence measurable or negative function and let we define F as series of u n. We have that the integral of F is equal to the sum, OK. So we want to use the monotonic convergence theorem, so it's quite clear how we proceed. So we define Fn as the finite sum and apply convergence theorem to Fn. And so basically you have that F is equal to the limit of Fn. Now you use the theorem. This is equal to the limit, so we take the limit outside the sine v integral and this is equal to the limit of y definition, sorry, of i, which goes from 1 to n of u n. And these are finite, so you can limit, OK. So this is just an application of the theorem. This one? Limit is not... Limit, ah, what is F, you mean? F is this. Ah, OK, yeah, yeah, yeah, OK. OK, you can, yeah, I mean, I just... It's the same, but it's just to emphasize the fact that you can bring the limit outside.  Yeah, yeah, yeah, sure. OK, and then... OK, this is another, somehow, consequence. OK, so let F be a non-negative function. We consider some disjoint set. The sequence measure the set and then we take the union of such a sequence, e, and so then we have that. So the proof, OK, this is a countable union, of course, this is... Just if you let define ui has F times the characteristic function as one of the set in the union. OK, then you have that F, q of v is equal to the sum of this ui and from the previous proposition or corollary, previous corollary, pathetesis. OK, now we see another version of the Fatus Lemma in which we, somehow, we require less in the hypothesis but, of course, we also get less. So, which I will not part with as Fatus Lemma in its second version. OK, so we consider, so let fn, a sequence measurable... OK, then we also have somehow of measurable non-negative function. OK, OK, that's it. So we don't require anything else and what we can say, we can say that the integral of the limits of fn, because now we are not even sure that the limit exists, OK, because we do not require any extra hypothesis about point-wise convergence, OK, is less or equal than the limit of the integral of fn. OK, so this can be proved, has... can be viewed as an application. Can I erase this? No, OK. OK, can be viewed as an application again of the monotone convergence theorem. OK, so we have that... OK, I use the definition of limits of fn is equal to the supreme of the theme of fk... k... No, sorry. k is less than n and less than n. OK. And then we want to consider this function here. Gn has this infimum and this is an increasing... this is an increasing sequence of function, OK, for the sequence, because basically I am doing infimum over less and less indexes, OK, in the sequence Gn is an increasing sequence of non-negative and measurable function and so on. OK, so basically we are under the hypothesis of the monotone convergence theorem, but before in this we have that this is an increasing monotone sequence of functions so it admits limit so it admits and we denote with f this limit so limit Gn which coincide with the limit of f of fn. OK, now we apply the monotone convergence theorem to Gn and so we have the integral of f over e is precisely equal to the limit of any tensor plus infinity of the integral of the Gn, OK. And now observe some inequality and then we are done. OK, so being Gk is equal to of fk larger than or equal to n this is lessor equal than fn. So we have that that OK, Gn is lessor equal than, OK, this is lessor equal than fn and from which we have that f is equal to the limit n which is lessor equal than the limit and so what we get, OK. So now we give an example that this is more about the monotone convergence theorem. OK, if you take for instance we require that the fact that we want to take the freezing function, what happens. Is it still valid or not? With an example we will see that it's not valid. OK, so an example to see that the monotone where this theorem need to hold for the freezing function for the freezing sequence of function. OK, so here we are within this domain in real line and we define the candidate to provide a control example are this function the characteristic function of the f real line of this portion of the real line. So we have that fn Is it the freezing sequence? OK. Is it the freezing sequence which converts pointwise to zero. So almost everywhere actually we wrote almost everywhere because it's enough, but the convergence of course it's it's everywhere in R. OK, but of course when you compute the integral of the limit function and the integral of fn you have that here. This is infinite this is plus infinity and the integral is zero. So here is the same convergence goes to zero for the same reason before. You fix some x if fn is sufficiently large then x fall into the domain where fn has value of zero. Now we introduce the concept of integrable function so we have that a non-negative measurable function of course f is called integrable over e for instance over the main of the set e is its integral e is finite this result OK, we start by f and g to non-negative measurable function we have that if f is one of the two is integrable over e and if the other one can be bound from above by this integrable one and g of x is less equal then f of x is raining x in e then OK, almost n e then g is measurable as well e is not measurable, it is also integrable and you can compute and you have that e of f minus g is equal to the difference between the two OK, so we have that we just start that we can split f as f minus g plus g and we pass to the integral and then we have that integral of f is equal OK, to the f minus g plus g and then we use in productivity this is equal to the integral of f minus g plus the integral of g but we know that we use this fact we have that f the integral over e over f of x minus g of x is bounded it is non-negative also g, the integral of g is positive and we have two and so since we need to use our hypothesis this one is finite then we have that by this relation we can deduce these are both positive some give rise to something which is finite so it must be separately finite then we have that it's finite, so g is integrable and moreover we are within finite quantities so we can take this and move it on the other on the other side of the equality OK, so we have that minus g and so we are done we will use all this fact to prove a theorem that is called the absolute continuity of the integral so it's somehow a version of continuity for integrals so you have that we start by non-negative measurable function which is integrable so we must know a priori that the integral is finite and then what can we say we have that in the definition of continuity we use epsilon and then delta then given for any epsilon positive that exist in delta positive such that if you pick a subset of e, a subset a of e which small measure less than delta such that for every set a continuity in e with measurable set a with measure of a less than delta then you can say something about the smallness of the integral of this integral function of a this is less than epsilon ok, so we start ok, we start we divide it into cases first we consider an easy case when f is bounded ok, so if f is bounded so we know that f is bounded the integral it is so we know that there exist some m positive such that f ok, we can get rid of since it's non-negative this is true ok, just to stress that it's bounded and so we have that f is of course is less or equal than m times the measure of a which is less or equal than m times delta so if you pick epsilon would be m delta so if you choose delta equal to epsilon divided by m we are done then we consider the case in which the general case which in principle f can be integrable but not necessarily bounded and so the idea is that we want to approximate general function an unbounded function by bounded one ok, so consider this sequence this sequence of bounded function that are defined in a piecewise way so they are they coincide with f of x if of x is in between 0 and n or you it's a kind of cutoff you put them to be equal to n otherwise so if f of x is larger or equal than n then maybe sometimes it's useful to observe that this one you can express this as the minimum between f and n so this is also a way to see that for instance it is measurable because it's a minimum between measurable function ok, fn converts f pointwise so almost everywhere in e ok ok, if you want it you can see that ok, if x is a point such that if so you fix x because we are talking about pointwise convergence if x is such that f of x is finite ok, then you have that that exists some n that depends on x such that f of x is less than this n and so you have that for any n larger than n bar fn of x is coincide with f of x for any x or otherwise if x is a point where f is not bounded is such that f of x is equal to plus infinity ok, then you have that fn of x is equal to x is equal to n and then you have that again fn converts to f ok and then again we want to use the monotone convergence theorem so we observe that it is increasing sequence of functions ok, so moreover we have that fn is an increasing sequence functions which converts to f so by monotone convergence theorem you have that the integral of f over e is equal to the limit of the integral over e over fn ok, then just rephrase this fact by using the epsilon delta definition of limit so you have that for any epsilon positive there exist some n some index n such that for any n larger than n you have that the difference let me be minus e fn this difference is always positive because this is increasing and which is equal for instance is less than epsilon over 2 for any ok, I already wrote so, now we choose our delta in the statement of the theorem to be equal to epsilon divided by 2 times n and we consider a set a and let a, such that the measure of a is less than delta so we want to estimate the integral over a of our function f and so here we use with sum and we subtract the same we use this this trick ok here you use the fact that these fn are bounded and here you use the fact that this difference is small this for instance ok, we can precisely take this index to be this capital N or in any case any index N larger than this capital N so this is less than the integral ok, overall fn plus this is n this is bounded by n times the measure of a no and so at the end what you get is epsilon over 2 plus n for our choice of delta this is epsilon divided to n so ok of course you end up with the fact that this integral is less than epsilon ok, so now so far with all this theorem of for instance of convergence under the sign of integral I mean the strategies was we know something about the point wise some point wise information about the function and we deduce some information about we transfer some of this information to some information about the integral of this function ok, so from point wise we study the integral so now the question is can we do the reverse so if we have some information about the integral of such a function can we deduce some point wise property some good hypothesis the answer is yes and you can you can this is a first example of this correspondence between the two information so you start by f again be a non negative measurable function ok and then we have this equivalence so we have that if f is equal to zero almost everywhere in our domain e so if and only if if and only if the integral of f is zero ok ok, one side is completely trivial no ok if you want you can formally say it as you consider in any h you can take the definition with those h so you will have that the integral this h of course is zero and so you have you have that the supremum of this function h that are involved in the definition of the integral of non negative function is zero so you have that also the integral of f is zero ok, this is the trivial part and so what about the other so we start by knowing the fact that the integral we know this ok, so we define this set a n as the set where f is larger or equal than one over n and so you can somehow reformulate this we have that that f is larger or equal than one over n characteristic function of a n ok so this is zero is equal to f larger or equal to one over n this integral and then this is one over n times the measure of a n and so you have that the measure of a n is zero for n n moreover you have that you take the union you have that the set where f is strictly positive can be viewed as the union we already saw this the composition the union of a set like this f larger than one over n and ok, this is our union of a n is a countable union and so we have that the measure of this set is less or equal than the measure of less or equal than the sum of the measure of this a n which is zero so we have that indeed f is zero almost everywhere in here ok because f is larger or equal to zero ok is not negative if we prove that f the set where f is strictly positive as measure zero means that f is zero almost everywhere and now ok, now we see somehow a related result which goes under the name of Chebyshev inequality probably you already know this ok, so again f is from e from set e to r non negative basically we have the same hypothesis before function not negative ok, measurable function ok, then for any for any t, for any number t positive we have the following inequality that you can estimate from below the measure of this set is kind of not level set but this set by one over t times the integral of f over e ok, the proof is quite is quite fast so how would you prove this we need first to consider something like this so we have that f is larger or equal than t times key f larger or equal than t ok, we start by observing that this inequality all and then as before we just have to pass here we have just to pass to the limit and you have that this is so equal than t times the measure of this set ok, so we are done the measure of ok, now always in the spirit to deduce some point wise property from some fact that are stated as integral property we prove this corollary, which is a corollary of the Chebicev inequality that tells you that if you have that f ok, it's again a function ok, no negative ok, measurable and you know that such that the integral of f over e is finite so f is integrable then you know that in this point wise fact that f is finite almost everywhere in e ok, so to prove this we want to estimate the measure of the set where f is equal to plus infinity and to prove that this is equal to ok, so we consider this set ok, again we already saw that we can express this set in this way so you have more than express you can say that this set is contained in the set which is involved in the Chebicev inequality and then by monotonicity ok, we have that the measure of this set is less or equal than the measure of this set here now we use the Chebicev inequality ok, that tells you that this is less or equal than 1 over t the integral of f this is true for any t and so we know that this is finite by hypothesis of since this is true for any t if you let t goes to plus infinity you get that indeed the measure of of this set is zero ok and so we are done and now we are in position to define the general back integral we start somehow with a new argument ok, so I recall you that so we already saw that you remember what is the positive and the negative part of a function do you remember? ok ok, so we will skip this part so from this you understand that how it can define the general back integral so we can split a function f any function f into the difference between the positive and the negative part which are positive non-negative functions so we know how to compute the integral and the natural way will be to define the integral of f as the integral ok we say that a measurable function f is said to be integral of f ok, if f plus and the positive and the negative part are both integrable over e in the sense that we introduce before ok and we define the back integral of function f over e as this quantity f plus f minus e f minus ok, now we have to prove the usual properties of the integral because when you give a definition then we need to see that the linearity holds and so on, so maybe we will start today and tomorrow we have f and g to function which are integrable over e ok, then we have these 4 fact ok the function c times f is integrable and you can you can take c outside sign of integral and then you have when you consider the sum f plus g is integrable and you have that the sum the integral of the sum is equal to the sum of the integral ok, then there is the monotonicity so if you have that f is less or equal than g almost everywhere in e then the inequality is preserved by the integral and finally the last one or consider to this joint set a and b this joint set then you have that a union b of f is equal to the sum of the 2 ok, we consider the first one if c is 0 of course there is nothing to prove or start with the case when c is positive the case c negative is analogous so you have that cf is now here we use just the definition we just if this is e c f plus minus e cf ok, then we have that for this integral you can write that e this is f plus you can take c outside minus c e f minus and this is equal to you collect c so you get what you want ok, the case c negative is analogous and probably maybe you can do it by yourself you just have to use this fact this is the positive part of minus f is f minus and in analogy the negative part of minus f is f plus ok so you have to use something you have to use this fact at some point ok, to prove the point two we start first by a general fact we will prove a general fact and then we apply it to our case so if we have in general if you have f which is the f1 is given by f1 minus f2 with f1 f2 non negative and integral function then you have that f is equal to f plus minus f minus is equal to f1 minus f2 ok, so by this we have that f plus plus f2 is equal to f minus minus f plus f1 so they are both side of this equality are non negative ok, and then we use previous result about the additivity of non negative function ok, so by previous result additivity non negative function ok, what can we say? we can say that f plus plus f2 ok, is equal to f plus plus f2 which is equal plus plus f1 is equal to f minus plus f1 ok, now we observe that everything is finite so all these quantities are finite because we are talking about integral function so we can write everything also all the integrals are finite all the integrals involved in this equality so you have that f plus minus minus is equal to f1 minus f2 so finally you get that the integral of f is equal to f1 minus f2 so you can use also this decomposition so in call this star ok, this is a general fact so how we use this for our purpose ok, so we observe that we have f plus plus g plus and f minus plus g minus are integrable and positive and satisfies all the good properties and so we have that f plus g is equal to f plus plus g plus minus f minus plus g minus so this is would play the role of f1 and this would play the role of f2 ok plays the role of f1 and this plays the role of f2 ok, so basically you have that f plus g is equal by star ok, again by f plus plus g plus minus f minus plus g minus and so you can collect in the correct way so you add that this is equal to this again because everything is finite ok, just see 3 monotonicity ok, we start by observing that f minus g we start by no, actually it was the reverse g minus f is larger equal to 0 ok, and then what we have ok, this is easy, so you have that just g minus f is coincide with part plus which is so by step we can use the linearity so we have that g is larger than f ok, and the last one is ok, it's very easy 4 ok, we have this this joint set a and b, so you have f you just use the fact that f times key of a union b is equal to the sum ok, f key a plus f key b ok, so we are done ok, for today we can stop here


Can cat 6a run gigabit ethernet? Cat 6a cabling is similar to cat 5e and cat 6 in that it is capable of 1 gig ethernet. This is for a 90 meters connection, again the same as cat 5e and cat 6 up to 90 meters for a permanent link. All structured cabling for copper links design is based on a permanent link of 90 meters and an allowance for 10 meters of patch leads in total. Therefore, for gigabit ethernet, cat 6a cable has no advantages over cat 5e and cat 6. Can I use cat 6a for 10 gigabit ethernet? Cat 6a is the cable of choice for any 10 gigabit ethernet installation. Cat 5e is not suitable for 10 gigabit and standard cat 6 is only capable at 55 meters. As all design should be based around 90 meters links, cat 6a cable is the minimum expected cable for 10 gigabit ethernet situations.


The Lagos State House of Assembly has approved Governor Babajilé Saint-Louis's request for the state to assume full ownership of Lecky Concession Company Limited. This was after the presentation of the Committee on Finance report during plenary session in Lagos on Monday. The House had received the request from the Executive on June 21. It's also a follow-up to buy out of all the shareholding interests in the company by the state government.


Hello and welcome to session 37 on our course on Quality Control and Improvement with Minitab I am Professor Indrajit Mukherjee from Shailesh J. Mehta School of Management at IIT Bombay. So, previous session what we have done is that we have seen 2 to the power 5 design like that. So, 5 factors at 2 levels now we will move ahead with ah number of factors ah k number of factors, but ah number of levels is more than 2 that is let us assume that 3 level ah design. So, 3 level 3 to the power k and in this case we can assume that simple example let us say 3 square design which we can consider over here. So, ah one example we have already done in 2 way analysis of variance that we will represent and how it is to be analyzed in Minitab factorial design and how to create the design that is important over here ok. So, this is a 3 square design we want to create the design in Minitab where 2 factors at 3 levels. So, minimum number of trial is will be equals to 9 that is written over here and if you want to replicate that one. So, that will be the multiplication over here if we replicate it 4 times each of these designs. So, the number of trials will be 36 like that ok. We will take one example that was previously discussed also and here also we we will just show you how to how to create the design in factorial ah how to create the factorial design when we have 3 k scenarios we when we have 3 k scenarios or ah k factors at 3 levels like that. So, ah here a material type is ah what are the factor let us say this is factor A over here and this is factor B over here and this is having 3 levels material type 1, 2 and 3 and this is having temperature range which is also ah 1, 2 and 3 like that. So, 3 level design and 2 factors over here that is considered one is material type one is temperature and the CTQ that response variable is considered is the ah effective life battery effective life over here. So, in hours like that. So, we want to see that how to analyze create the data sheet and how to analyze the data into Minitab ok. We are interested into AB and AB interactions over here. So, in this case and what should be the final conclusion based on the experimentation that we want to see ok. So, how do we create the design that is important 3 k design how we are creating in Minitab. So, I will open a ah blank excel sheet ah blank Minitab sheet over here and we will create the design. So, this is stat over here and design of experiment. So, what we will do is that factorial design create factorial design and in this case we cannot select two level factors over here. We have to select general food factorial over here number of factor is 2 there is no problem with that and in design what we have to do is that we have to mention the number of levels over here. So, this can be changed I have made it 3 and this is also 3 over here AB factor. So, A can be we can we can mention this as ah material and the next one can be considered as temperature over here ah this is temperature ok. So, ah number of replicates if you see the experimental trial that is done over here. So, here you will find that there are 4 trials that is done for a specific combination. So, this is material type ah 1 and this is low temperature and I have 4 observations over here. So, this is 4 number of replicates 130, 155, 74 and 180. So, this is a ah 4 ah replicate design like that. So, what we can do is that we can we can just see this one and mention that number of replicates is there ah we are not concerned about blocking over here. So, we will ah we will just ignore that one at present scenario. So, this is ok and then in factors what we can do material type over here. So, either I code this one as minus 1, 0 plus 1 that is in ah coded terminology if you are if you are using the arbitrary symbols like minus 1 plus 1 what we have used earlier also and only thing we will mention whether it is tech. So, this is categorical variable. So, we can mention material type and temperature was considered as low ah medium and high like that. So, this is also categorical it has three levels. So, either I keep what is what is the level that is mentioned 1, 2 and 3 and low, medium, high we can write over here we can also write minus 1, 0. So, coded variable we can also mention like that. So, this is three levels, but in this case this is categorical variable both are considered as categorical variable. So, I click ok and in the factors this this is done and in options what we will do we will not randomize this one. So, we will not randomize the design. So, ah so, ah this we will we will click ok. So, number of factors. So, everything is done. So, design is created over here. So, you see standard order and unorder is same because we have not randomized. So, 36 number of trials this is the summary of the design this is created. So, whenever this is created we can we can just put the CTQ values over here which is the battery life and then we can analyze this one. So, I have created I have shown you how to create the design then what we will do is that this data is already with me. So, unnecessary we are not creating another we will not write down the CTQ values over here. So, we have the data set and this is the data set that we are having and we have entered all the 36 data points over here. So, now we have to only analyze. So, first combination is minus 1, minus 1 that is 130 that is the data set that you have seen this is 130. So, this data set is recorded over here. So, ah this we want to analyze. So, now I will go to stat I have created the design and this I will go to factorial design then go to analyze factorial design over here. Then you mention which is the response variable this is mentioned over here. Then in terms I want to see all up to interactions over here. So, I will I will mention 2 over here include terms and so this will be ok and graph we will have Pareto plots to see this one which is effective which is not effective like that AB or AB interactions like that. So, other things we will keep as default. So, we are not changing anything we are not using stepwise regression. So, we will click ok over here ah when we do that. So, A is 3 levels and this is the factor information analysis of variance table we can see. So, over here that will tell me that which is significant which is not also Pareto plot is there. So, in excel we can just paste this one to enhance the image and try to see what is important what is not. So, factor A is having a p value which is less than 0.05 A is significant B is also significant over here and AB interaction is also significant over here less than 0.05 All the factors and their interaction is significant over here. So, in this case what we will do is that we will go down and try to see R square adjusted value is 69 may be some other factors we are missing over here ok. But that is not of concern to us and we at this at this stage these two factors are important or not that is important. So, in effect analysis Pareto chart what we are seeing is that AB and AB interactions significant because this is 2.05 and every standardized effect is more than these values like that. So, all the variables are important AB and AB interactions. So, first order interaction is important. So, then what we can do is that we can just see graphically analyze this one. So, what we can do is that either go by this analysis and see the interaction plots like that and in that case battery life we have to enter and factors you have to mention and which are the factors A and B factors over here. This way through interaction plot and you click ok then you will get the same graph what we have seen in two way analysis of variance over here. So, the same data can be used for interaction plots like that. So, over here what you what you are observing over here is that and this is the best combination. So, minus 1 combination. So, this is the highest battery life what we are getting. So, minus 1 combination which is basically A at level 0 over here. So, that is material type 2 over here and then what we have is that temperature this minus 1 means this is the low temperature combination. So, the material type 2 and low temperature is the best combination, but what we mentioned earlier also in our lectures like that and this is more stable what we are seeing over here this is more stable. So, material type 3 is more stable. So, minus this 1 means 3 over here. So, this is green line what you are seeing over here and this is stable throughout the range of this is low temperature range to medium and and also high high temperature range what we are seeing is that battery life is always higher than any other materials that we considered. So, we may select material 3 in case we are unable to consider temperature we cannot control the temperature and and this is the most robust material we can use which will take protection against this change in temperature like that. So, this is one combination and this graph that you are seeing on the below part of this this will also lead to same conclusions over here. So, this graph also you can see from this. So, if you go to design of experiment factorial plot and factorial plot when you do this and you click this one you will get the interaction plots this is given over here what we have seen earlier also. So, this is the same graphical interpretation now you can predict the behavior what will be the response on this. So, I can predict also over here. So, if you say which is the level I will choose over here let us say I choose material type 3 over here and for the B combination over here I take minus 1 low range that is the combination I want to see and I click ok then I will get the settings and I will get the mean effective life that that is generated over here. So, that is the prediction values over here. So, the predicted value will be 144. So, predicted value will be and this are the prediction interval confidence interval that can also be seen over here ok. So, this is what we wanted to discuss some of the aspects of 3 square design or 3 2 power k we can we can create the design and we can we can see other examples on this also, but we will we will skip this and we will go to a important topic which is known as local control ok. So, I mentioned that 3 things are important in design of experiments one is randomization, one is replication and the third one is local control which is also known as blocking principle which is also known as blocking principle over here and that we that deals with the noise or nuisance variable you can think of ok and we are not interested in those variables basically. So, sometimes what happens is that while learning design of experiments we are not able to learn the complete batch and not a single supplier provides all the materials like that. So, we may have batch wise materials and based on that we have to we have to do the experimentation in sequence like that ok. So, so different batch of material may not be homogeneous. So, there can be heterogeneity in the batches in that case what happens is that this variation in the raw materials can impact my CTQ values like that. So, in that case we will try to block this variation we will try to block this variation and then we use a principle of blocking and while we are doing analysis of variance. So, we can we can separate this variation and we can see actually the factors that we the controllable factor which we have considered whether it is affecting CTQ or not. So, until and unless we block this what may happen is that the factor may not be showing significance although it is significant for the CTQ like that. So, that can happen and I will show you the examples ok. So, sometimes what happens operator to operator variation is there, but we are not interested to study operator to operator variation we are interested in studying the factor A whether it is significant to the CTQ or not. So, while screening the factors we we will try to see that ok, but we are not interested in but this can operator can influence the results like that. So, we have to block that operator influence or remove the variability that is due to the operator and then we will study whether the factor is important or not. So, ANOVA analysis can be used for that. So, blocking principle is used for that to understand the variation for blocks and if we if we if we can isolate that one then actual factor whether it is influencing CTQs or not that that will be clear ok. So, here also some examples time of the shift can also create trouble and so we we may have to deal with that and and block that variations due to due to shift or due to particular time of the day like that ok. And test samples that is used that can also be also can vary. So, that can also be a blocking blocking factor like that. So, that can be these are nuisance variables we have to understand these are nuisance variable where we are not interested into this, but we we will if we do not block this one that will impact the results that is why we are blocking this one ok. So, some more examples like when we are advertising like that. So, it is effectiveness and its impact on customer purchase intentions like that. So, if if a type of advertisement, but that will also there will be some variations due to main main and female response like that. So, that is we are not interested into that we are interested into whether the advertisement is affecting the customer's purchase intention that is our objective, but main and female or main and female can respond differently. So, that variation we have to isolate and then see whether that addressing is effective or not. So, that is also another example where we can apply these blocking principles like that and whether it is manufacturing or service people can use blocking principle while using design of experiments like that ok. So, there are basic things that we that we try to do when we are using the blocking principle if the nuisance variable or noise variable is known and controllable we try to block this like what material to material variation or supply to supply variation it is known and we can control that one in real life. So, in that case we will use blocking principle and sometimes what happens is that it is known and uncontrollable. So, we have no control in the environment or certain other scenarios, but we have to deal with that. So, if it is known if I know about that variation and it is uncontrollable sometimes the concept of Taguchi's robust experimental design is used and we will discuss about Taguchi's experimentation after after few sessions here ok. So, Taguchi's robust design. So, that can be used when known and uncontrollable when it is uncontrollable and unknown like that I have no no information or clues about these nuisance variable or noise variables like that which impacts the CTQs like that randomization to minimize the effect of that what we do is that randomization. So, that it is uniformly distributed throughout the experimental experimental results like that. So, we try to balance the impacts like that. So, that is the objective of randomization that we have mentioned earlier also ok. So, here we are dealing with blocking principle where we it is known and controllable that is the scenario. So, I will take one example to illustrate this one example. So, there are four different tips four different tips. So, our our objective is to study these four different tips which is measuring the hardness of or Rockwell hardness tester of this material like that and there are different test coupons that I use over here. So, I have a different test coupons 1 2 3 4 like this and each of these test coupons we can measure the hardness by using any of these different types of tips over here. And and this test coupons can also vary that means homogeneity between the test coupons is we are in doubt like that. So, in that case what we will do is that we will try to block this test coupon variations over here we will try to block this one and we want to see whether the if I change the types of tips whether the readings are changing basically or a hardness concentration hardness reading is changing or not or Rockwell hardness measurement is changing or not. So, what we can do is that each of this test coupon we can we can we can assume that this is one block this is second block this is third block and this is the fourth block like that each is treated as a block over here. So, blocks this test coupons are blocks over here and there are four levels of this block this is one level two level three level it is like two two factor experimentation basically. So, block is another factor we can consider over here although this factor we are not not so much concerned about that we want to see influence of this factor on the hardness reading whether it is differing due to different types of tips that is our concern like that if it is not then any of the tips can be used to measure the hardness like that that is the overall objective of experimentation over here. So, test coupon is the nuisance variation that that because of the heterogeneity between the test coupons. So, we have to block this in experimentation we are not interested in the block variables we are interested in the factor which which is considered over here which is type of tip like that ok. So, how to analyze this one? So, in this case what will happen ANOVA analysis will be used like that. So, treatment effects of all this factor over here what we have concerned different types of tips 1 2 3 4 like that and and these are the block variables these are the blocks that is considered over here. So, in this case what what our theory says is that we can also estimate what is the mean square block effects like that. So, in that case mean square block effects like that and mean square error can be calculated and this can be isolated. So, MS treatment MS block. So, SS treatment SS blocks and SS error can be calculated like that and MINITAB will do it automatically for you and then it will show whether the factor is important or not. So, this is the analysis that was done in MINITAB and then we will see that whether type of tip is significant or not yes it is influencing the mean values all the means are not same if I if I use the different types of tips and block which we have considered that variation is also also I have isolated over here. So, in this case what happens is that when we have isolated this one this is coming out to be significant that means test coupon to test coupon there is variation like that, but we are not interested in the block variable over here and only we are interested in this and that is this is coming out to be significant. Now, let us try to see this data set and try to see the analysis how do we do it in MINITAB. So, in this case what we will do is that we will see that example where we have selected. So, this is the example where we have already created. So, type of tip hardness measurement and this is blocking these are the block factors that is test coupon is considered as block over here we can analyze this this is a balance design over here. So, in this case what we can do is that we can just analyze this one using analysis of variance and balanced analysis of variance over here. So, we have taken the hardness as the over here and in this case what we have done is that type of tip and this is block which is which we have considered over here and this graphically we want to see if we want to see the residual plot that is possible and what we are seeing is that type of tip and block variables are considered the assumptions over here is that type of tips and block does not interact like that. So, interaction is not significant over here that is the basic assumption that we are making when we are doing this blocking principle when we are implementing the blocking principle we try to minimize the effects of blocks and interaction between types of tips and blocks over here. So, that is why I have not considered interactions over here. So, in this case what we what we will do is that this is blocks now if you do not consider this as blocks and consider randomized experimentation. So, here we are not randomizing that is why we are blocking and if I consider random experimentation we will just drop the block variables over here. So, what I will do is that ANOVA analysis one way analysis of variance we will go because there is one factor we are considering. Let us consider this is the hardness one and factor is type of tip. So, let us try to see what comes out of this analysis. So, when we make this analysis over here the ANOVA analysis that you will see copy pictures and we can paste this one. So, this we can eliminate and if we if we place this one what happens is that what I am observing over here is that type of tip is not significant you see p value is more than 0.05. So, if you are treating them in isolation and considering that all test coupons are homogeneous in that case what is coming out the results that is coming out considering only type of tip it is not coming out to be significant. But as soon as you consider as soon as you consider that the block variable yes it has influence. So, we should eliminate that variation. So, in that case what we have done is that we have considered that also as a factor and when we analyze that one what we have found is that we have found that this when we consider this one then it comes out to be results seems to be very different. So, types of tips is now significant and earlier it was 0.22 now it is 0.001 that is significant it is coming out because we have considered this block as another variability that that we have tried to isolate over here. So, we have to apply blocking principle in case we feel that some of the variables are nuisance variables that can impact the results. So, blocking is one of the aspects that is considered in experimentation that is considered in experimentation like that. So, this is one example we can take there are other examples also that is given over here. So, in this case we can take another examples. So, this is chemical and fabric and strength like that. So, in this case we can we can consider this and we can we can use the balanced Tanova analysis. So, strength is the variable let us say this is the y characteristics that we are and chemical and fabric is the block variables that we are using. So, different chemical types and fabric is the block variable that we are using over here. And in this case what we are we are not considering interaction effects, but we want to see. And here what we are seeing is that both chemical and fabric. So, we have blocked the fabric variables like that then only chemical is coming out to be significant like that. So, we can do individual analysis one way analysis of chemicals over here that may come out to be significant and may not come out to be significant. But when we have blocked the fabric variation due to fabric over here which is blocked over here in that case whether I want to see whether chemical is influencing the strength or that is the main relationship I want to see I am not interested into fabric over here. So, that that is the block variable we have considered over here. So, that way we consider the principle of blocking in our experimentation and this is used extensively. So, now how do we implement blocking in factorial design? How do we create that blocking in factorial design? So, I am trying to take an example where where the scenario can be we can use this one. So, there are let us consider factorial design you have done. So, factor A and factor B over here and these are the replicates. So, this is one replications that you are seeing this is one replicates second replicates third replicates. And but what we can do is that that the condition that is given over here therefore, three batches of raw materials are used over here. So, this means only four from one supplier we have got like that. Seconds is coming from second supplier third is coming from third supplier like that. So, supplier to supplier variation is expected over here the material that raw material that comes while we are experimenting with the factors. So, I am in doubt that the supplier to supplier variation will be there. So, in that case my objective is to basically block this variation my objective is to block this variation block this variation. So, each of these replicates will be blocked like that. So, that how to create that design. So, there are two factors over here. So, two square design. So, this is a two square design with three replicates. So, this will be multiplied by three 12 experimentation, but each of these four will be created as a block like that then only the analysis becomes meaningful when we when we are treating this because it is coming from different suppliers like that one batch is coming from different suppliers. So, factor is reaction concentration factor B is catalyst over here and we want to see what is its influence on the yield like that. So, let us create the design and then try to see analysis how we can do the analysis ok. So, how do we create blocks in factorial design? So, what we have to do go to stat design of experiments factorial design create factorial design. So, let us say this is a two square factors like that number of factors over here. So, then you have to mention over here that how many number of blocks. So, number of replicates over here is 3 and then number of block is over here I am creating is 3. So, when I create and set up point we will keep as 0 over here we are not concerned about center point at this time point. So, then we can write down the factor A and factor B whether it is numeric or text like that. So, that you can mention like that and in options we will not randomize the run and also we will not fold the design like that. So, folding is when we are doing that fraction of factorial that will be used. So, randomize the run we are not randomizing this one. So, standard order and run order will be same. So, in this case when you click ok what will happen is that blocks will be created in the design. So, blocks will be created.  So, one replica one one one set of observation is taken for complete trial is done by let us say a supplier 1 like that that is treated as block 1 then block 2 and block 3 like this. So, when you have created the design and then mention the CTQ values over here. So, when you mention the values over here and then we can analyze the data like that. So, I have the data with me. So, we do not need to do this because we have already have this data sets. So, let me try to see where it is. So, here it is data set is over here. So, here if you can see this trials over here. So, all the data sets are 12 data points that is collected over here. So, blocks you can see first block second block and third block like that. So, block is already created like that. Now, I have to only analyze the data what we will do is that stat design of experiment factorial design and then we will analyze factorial design response is yield over here term we want to consider AB and AB interactions over here. So, here you will find that include blocks in the model. Yes, we want to include the blocks in the model that is ticked like that and then para to plot all these things are possible and other things are default what we are not changing over here. So, when we do that what happens is that I have a ANOVA analysis over here which will indicate that whether blocking has helped or not. So, in this case we can we can just copy paste this one and delete the earlier information. So, we can just copy paste this information and we can just enhance this one. So, model is significant, blocking is not significant although the we thought that supply to supply variation will be there, but the p value indicates that the homogeneity in the so, block to block variation is not so prominent over here and not statistically significant, but always we prefer to block because whenever there is in doubt you should block. So, then what happens is that because we have so, we have taken care of this blocking principle over here then whether factor A and factor B is significant, DCT is significant interaction is not significant, interaction is not coming out to be significant and that will be also prominent when we study the, when we study this this para to plot when we study this para to plot. So, here where is that data points and this is yield and in blocks. So, this you can see so, this is standard effect plots that we para to plot say B is not coming out to be significant over here. So, what we can do is that settings of this variable what we can do is that only by factor plots like that. So, if we want to set this one we will go to factor plots and click ok and then only the main effect plots can be used like that interaction is not prominent. So, we want to maximize the yield. So, in that case combination will be minus 1 and this will be B will be at plus 1. So, that is a combination that we will use ok. So, that is the way we will analyze. So, in factorial design also we can implement the blocking principle we can implement the blocking principle over here. So, that is the one aspects I wanted to mention like that and there is another aspects that when we are doing design of experiment another one aspects is coming several times that is known as center point that we have not discussed. So, this is the block design what you are seeing block 1, block 2, block 3 like this and this is the analysis that we are analysis that we have shown and these are the interaction plots and we can also check the residual plots like that and this comes out to be normal and because these lines are parallel no interaction this is the interaction plots that you are seeing and because A and B is only prominent. So, we can only see the main effect plot and that will give me the combination that that will maximize the yield basically ok. So, general guideline whenever you are in doubt like you try to block that one and block the noise variable in case you know about it randomize in case it is unknown noise or unknown reasons variables like that. So, it is good idea to conduct the experiment in blocks where complete experiment cannot be finished. So, like what we said that it is coming from different suppliers like that. So, in that case we use the blocking principle like that ok. So, blocking is one of the principle that I want to highlight and also one important aspects that is center point we we try to add center points in the design of 2K design let us say. So, how does it help we we are moving in design of experiments let us say sequential experiments from one region to the other region like that and whenever you are at the optimal point what happens is that you will find curvature. So, if this is the y variable and this is the x region like that. So, you will find that optimal reason may be over here. So, this is the point which is optimal over here because whenever optimal region comes then there will be there will be some curvature in the model like that. So, that is expected let us say this is a function that we are seeing over here. So, this function that we are seeing over here. So, in this case what happens is that we want to see that maximum point is over here. So, if this is the region that I am experimenting over here. So, in that case it is expected the second order model will be more effective as compared to the first order model or response surface can be built like that. So, in that case what is important is that we try to add center points whenever I am in doubt that whether we are in the region of optimality. So, in that case what happens is that then the model x square terms become prominent like that. So, that can be studied if we are adding center points like that in the design like that. So, what happens is that center points will be added over here. So, this is the experimental zone of factory and factor B minus 1 plus 1 and for the factor B is minus 1 plus 1 there will be some 0 points over here that will be taken like this 0 points over here and some replications will be done in the center points over here. And in that case average of the corner points will be compared with the center point values over here. So, average of this and if there is a difference that will be reflected by this SS pure quadratic term whether it is required or not. So, that means, whenever there is a curvature it will be reflected like this. So, whenever there is a curvature the average of this will be different from the average over here. So, average of corner points will be different from the center points average like that. So, when it is significant when this difference is significant it will the P value will indicate like that. So, here when I do the ANOVA analysis of curvature what I am getting is that P value is significant over here and in that case that indicates that the model requires we need to add more square terms in the model maybe a square maybe b square over here ok. So, that is the term we need to add to get a better models like that. So, whenever I add a center point I want to see whether there is a curvature in the models then we will use certain other designs to get the get the fundamental models of adding the square terms like that ok. So, those things we can see. So, we are adding center points to understand that whether we are in the region of optimality whether we are in the region of optimality or not that is the main idea. If we are in the region of optimality then we can use central composite design to get the response surface basically at that point. So, that is that comes under the purview of response surface design because when we are near the optimal point then we try to use some high end design like central composite design to get the response surface equations like that which can consist of a b and a b interactions it can also consist of a square and b square terms also we can we can incorporate that point. So, this center points we can create like that. So, if we if you go to the center points like that. So, if you if you go to any any fundamental design like that. So, in this case what we can do is that we can add center points. So, design of experiment factorial design and we create the factorial design. So, when number of factors let us assume this one two square design we are assuming over here. So, in design what we can do is that number of center points. So, if I want to add four or five center points like that. So, that is a number of replicates over here number of blocks let us say we are not blocking anything. So, if we create like that and we create like that what happens is that there will be some combination four points that will be center points over here. So, a b combination will run and also that zero points will also run over here. So, this when I when I measure the CTQ values at zero points also we can have an estimate on the center point y values and that will be used to see the corner point average with the this one. So, this this value will be calculated. So, this SSPO quadratic will be calculated and that will tell me whether curvature is present this p value will indicate whether the curvature is significant or not like that. So, this is also sometimes we we try to check when we are near to optimality or not like that whether we have reached optimality. So, mostly used in response surface methodology mostly they will try out say adding center points and then going to CCD design whenever we are near to optimalities that scenario is mostly we add center points like that ok. So, we will stop over here we will continue in some other topics from here. Thank you for listening.


Hey everybody and welcome to my October budget. As many of you know that have been watching my channel for a little while and also follow the plan with me videos, you would know that this budget is going to be way different than any of my other budgets because unfortunately on September second, which this kind of ruined my budget for September but we're not working on that, we're working on October this time here, I was laid off from my job after almost nine years.  So anyway, so yeah this is going to be a little bit of fun. All right so I really don't have, well we're gonna get into it, let's write October budget and then I'll keep, I'll keep yammer in our way and bugging you guys. Okay so I've got my little thing written down there. Gosh it's so hard to see on the viewfinder. I don't have any lights anymore, like I've already packed everything and it's already gone so yeah. I'm gonna use some washi today, this is like from Scotch, it was actually from Target last year during like Halloween time. I think I got it on sale actually because I don't really buy a lot of seasonal things, I mean unless they're on sale so yeah. So that's exciting but okay yeah so getting back to the story, yes I was laid off so I am now filing for unemployment so I've got that underway, however I haven't been paid anything yet because they did pay me a month severance pay so I'm not sure how that fits into unemployment, however I'm still you know like abiding by all the rules of unemployment, still looking obviously I'm looking for employment, well duh. But yeah so I really don't know like my legit October budget, I have no idea what incoming money I have at all. I do know what incoming money is going to be coming in from my part-time job but I have no idea what's coming in from unemployment so yeah. I still can work my part-time job, I just can't work over a certain amount of hours but that's okay because my office that I worked at, well not office but it's a retail location in Fargo. By the time you're seeing this I will probably be moving in the next day or two but I am transferring to the St. Cloud area in Minnesota. It's not technically Minneapolis St. Paul but it's closer to where I'm going to be living for a little while and they only have part-time availability for me anyways so it's fine, it's all good. So at the top as usual I'm gonna put in what I know is coming in and then I'm gonna write out like my list of bills. So I'm just gonna write part-time and I get paid twice in the month of October from the part-time job. I think they're gonna be about the same, I think they're gonna be both at around like the $200 mark. I don't really know but you know it depends on what shifts they give me. Sometimes they'll give me like a four-hour shift, other times they'll give me like an eight or a nine-hour shift so I don't really know and that's all I know that's coming in for the month. However, things are taken care of so that's good. I have been following the Dave Ramsey plan for a while. I'll leave the link to his YouTube channel below if you guys want to watch him. I have already completed Baby Step 3 which Baby Step 3 is a fully funded three to six month emergency plan as well as I already started on Baby Step 3b which is saving for a house. So I am not too incredibly worried about money. I mean yes it would be nice to have more come in. I totally get it. However, I have enough money to live if unemployment doesn't come in for a little while or it takes me a while to find a job. I just don't have that anxiety about money because I've been preparing to actually purchase a home. Thank God I didn't purchase a house in this town but anyway I'm still in Fargo as I'm filming this because honestly this is not where I want to be in life. I don't want to be in Fargo. I moved here for work. Work ended. I'm leaving so that's a good segue into where I'm going to be living. So my parents actually have a summer home in Minnesota and that is where I'm going to be staying. All the expenses are paid minus a couple utilities which I'm going to take care of so I'm going to put those in at least what I know of right now and then you know I can pay it as I go on. So let's put in some of the fixed expenses that I know about and then we'll just keep you know going on. Okay so I'm actually leaving my apartment that I'm currently sitting in right now and my lease is up on October 31. However I've already prepaid for all of October and everything so I don't have to worry about that in October so I do have to pay my health insurance. It's like the Cobra insurance and that is $311.15. I've actually already paid for the month of October because it's due on the first but this will be like for November if that makes sense for you guys and actually let me zoom you in a little bit closer. I feel like it's so far away sometimes when I'm like writing out this stuff so anyway you get a really good view of my nasty nasty cuticles because that's what happens when you move guys that's what happens. Okay so health insurance is a given my cell phone is the same each month 62.55 my insurance actually I need to change over by insurance since I am actually leaving the state so I actually have an insurance friend in the state of Minnesota that wasn't licensed in the state of North Dakota so he couldn't you know help me with my services in North Dakota but since I'm moving I'm gonna go see him and then obviously I need to get different insurance because I'm insured in this you know in North Dakota and not Minnesota so my insurance amount will probably change I just don't know so I just need to actually look up and see how much my insurance is like an auto pay so I don't ever remember how much it is it's like a hundred something every single month and sorry I'm like kind of ill prepared a little bit ill prepared today let's see here we go reoccurring bill pay all right 109.68 all right and then my netflix I think netflix finally went up to 9.99 a month which is fine um it used to be 7.99 for all the streaming but I think it's 9.99 now yep 9.99 okay it just changed um I'm not too worried about the two dollars guys seriously but I know everyone was kind of up in arms about it but I think it's gonna be okay and then also um I'm disconnecting everything here when I leave but I still will have to pay a residual electric bill I'm not sure how much that's gonna be I'll fill that in in just a minute and then also um for October I won't have to play a cable bill here or not cable but like a wi-fi bill here in Fargo but I am taking over or not taking over I'm like starting a new wi-fi service at my parents place because apparently they had like a hotspot and it just isn't working especially for like video uploads and netflix streaming and stuff it just doesn't work out um there's a $50 installation charge and then I think it's going to be around the hundred dollar mark the first month and then after that it should only be like 50 something with tax and fees and stuff but anyway that's just like a one-time fee so um I'm going to budget for around $100 which is just fine and then the electric I'm pretty sure is going to be around the $50 mark I can't imagine that it's going to be any more than that so I'm not going to be putting my master card on here um what I do with my credit card is I actually pay it off every single month like in full and I usually just use it for like fuel for my vehicle sometimes groceries but just to put something on it this month that we're currently in I was really conscious not to put anything on the credit card at all because I knew that I had obviously been laid off from my job so I just didn't want another bill coming in so that is not going to be on this budget because obviously then you pay for it in the next month other expenses I have coming up in October I'm actually going on vacation oddly enough um I've already paid for a flight so I'm still gonna go and it's actually to go to a family wedding in Florida so I'll be staying with my parents and because that's where they normally live so I was planning on doing that anyways so really the out of pocket expenses is going to be pretty much nothing I mean I might use some of my going out to eat food budget or something like that but honestly I don't need anything and I'm only there from like a Wednesday to Sunday and really I'm just going to be hanging out with family and friends so I'm not too incredibly worried about that so under all of these fixed expenses not fixed expenses but pretty fixed expenses I'm going to put like my cash for what I usually do I'm not going to put anything in the clothing budget or anything like that so this month we're just going to do food and then usually what I end up doing is groceries so like grocery food and then like eat out food and I'll actually probably use some eating out food budget because I have friends that live in the area that I'm going to be at so that's exciting okay so my grocery budget for the month I always like to do around $200 they feel like that's good for me especially um you know I usually go to the grocery store every week but a lot of times I'll do like one big trip and then um every week I'll go but I'll get like bananas and fruit and veggies like the fresh stuff and sometimes bread but I'm not really big like bread eater so I feel like $200 is just fine for me I feel like some people always comment like $200 while I can never make it work but think about it it's just me you guys like if you were to be a single person that didn't have any dependence that wasn't married or didn't have multiple people in your household you could probably work off of $200 um and then my eating out budget is going to be about $100 I'm giving myself a little bit of extra leeway there just because I am going on vacation too so that's really my only like cash that I need for the month and I can tell you I have so much cash right now because I have been selling stuff so I won't actually like need to go and get this cash at all so and I'm actually trying to see if I can pay some of these other bills in cash because it's ridiculous like I sold my sectional I sold a bunch of other furniture and just regular like home accessories and mirrors and wall hangings and just like I've been selling so much stuff and cash is a fantastic thing I completely agree with that statement but oh my gosh it's getting ridiculous y'all but it's okay but because I'm still budgeting with that cash so I'm not too worried about it plus I also have my emergency fund and things like that too so let's get this all totaled up and let's see what we got for the totals here so just to cost me to live is going to be $643.37 um minus the food oh you know what I should also put is um uh gas for my vehicle I usually budget around well actually no October I won't be doing any extra traveling so I should um budget around the $100 mark I am going to be in a larger city so things are farther away so yeah that should probably actually go up here but that's okay we'll we'll get it figured out so really and then this is around like the $400 mark down here sorry my phone's breaking out okay so my total is this okay minus the $400 that I'm possibly expecting from my second job so really I need to come up with the $643.37 which is living pretty minimally if you ask me at my parents place that I'm going to be staying at for a little while I don't have to pay rent which is nice but I will probably be taking over some of the utilities and stuff like that too um pretty minimal expenses especially once unemployment kicks in if I haven't found a job by that point so yeah but I am still looking and still trucking on so I think that is going to be it for the October budget I hope you guys enjoyed I know that this is kind of a weird budget because everything got so screwed up from last month I will be leaving a financial playlist in the bottom bar below if you guys are interested in any of my other like finance talk things and if you guys have any like tips or tricks on how to budget a little bit more conservatively when you are going through a layoff or a job loss put them in the comments below I would be really interested to see um feedback of what you guys either have done for yourself when that's happened or like just ideas that you might have if that were to happen to you so I hope you all are having a wonderful day make sure to give this video a thumbs up if you liked it and subscribe I'm here every Monday Wednesday and Friday so I'm gonna let you guys go for now but I will talk to you all in my next video bye guys


I call Mr. Emil Bock from a local and regional authorities. You have one minute. Europe is a top-down and bottom-up process. Top-down is about the institutions. Bottom-up, it's about our citizens and about our local and regional authorities. Now it's time to consolidate our European project, listening more to the voice of our citizens and to the voice of our local and regional authorities. We need more communication with the people, not just the communication to the people. From that perspective, we emphasize the importance of education. Education and culture are the best antidote to intolerance, racism, populism and ignorance. Education is the best way to get out of poverty, and there is no risk of bankruptcy, no matter how much money you invest. Access to education for all and reducing the local and regional and national disparities in the field of education are one of the best methods to make our Europe stronger. I would close with the conclusion of Jean Monnet. The nations of the past are no longer the framework that can solve the problems of the present. And the Golden Rule, it's better to discuss around a table than on a battlefield.


Hello, NJRoot22.com here with the special Thanksgiving Black Friday edition of the supermarket roundup. I'm filming this on Thanksgiving morning before we head out into the events for the day, but I was going to do this last night, but let's just talk about it. It's a kind of a pact with flyers this week, so what am I talking about? Let's start off with Kings. Not impressed. Again, they have this big front and center, hot deals for Black Friday week, whatever that means. As always, there's really nothing to write home about. There's a couple I will point out though, however, they have the LaCroix, that's a good deal. If you like orange juice, they have their orange juice. Black Friday comes at the $2.59 ounce container. Another thing I saw that was pretty decent is they have the Bell and Evans Chicken Nuggets for your kids. Those are half price, basically, $7.49, excuse me, Jesus, for two packages. Next is, we're going to quickly talk about IGA, which is Bishop's White House, Pennington Food Market down there, on Route 31. Really not much to write home about, either except they have organic blueberries for $2.99 a container. We think that there's an ongoing debate in here. Does organic really, really matter, or is it just something you do to feel good about yourself? Because what, 70% of the organic products tested had some sort of non-organic pesticides or whatever on them. I don't know. Hatfield Bacon, it's not our favorite, one of the worst, but $2.99, you can't go wrong to save money. They have these Meat Franks, Hatfield, again, not one of our favorite brands, but it says selected varieties are $0.99. You'll see inside that it's not the beef Franks, I think it's just the chicken and pork Franks. This is interesting, IGA here is touting, it's the store brand that's name brand. Are they saying that the name brands make all their things, sort of the way Aldi does? They got some organic stuff on sale here. You could see strawberries, frozen strawberries, it's always good to have in the freezer. Here's the Hatfield, you can see the beef Franks are $4.00, so beef Franks, I think, taste significantly better when you eat them by themselves. I don't use buns, so that makes a difference, you can really taste the difference. Stop and Shop, I say no, I'm not a big fan of Stop and Shop, even though they're pretty close by to where we are, we're not a big fan of Stop and Shop. Until we find a good reason to go there regularly, we're not going to give them much attention here, but they do have a good price on lean ground beef, which is $1.99 a pound when you buy it in their value pack, probably 3 or 4 pounds. Here's something interesting, one of our favorite stores out there to find good deals is Ocean State Job Lot, and they have their typical Black Friday sale going on here. It's not as good as I thought it would be, but they have some things that are almost like no-brainers to buy if you want to save some money. I recommend using rechargeable nickel metal hydride batteries for all your toy needs, but here's something, you get 32 batteries, double layer triple A alkaline Panasonic batteries.  It's always good to have some throwaway batteries in your arsenal, just in case you don't want to care about recharging them or not losing them. Here's some good deals, I'm going to buy this, it's an omelette pan, it's one of those copper omelette pans, it's 10 bucks, you get a $10 card, but I always wanted to try, I can make eggs and omelettes without it, but it would be nice to try it, even if I throw it out or it just takes up too much room and ends up in the basement somewhere. It's a free way to try it, and here they have their copper pans, they're not the best, they're not like brand name and they won't last forever, but if you need to make little loafs or pies or things, you pay 15 bucks worth of those, you get a $15 card for it. Here's some other good ones too, these art supplies in the middle, these artist pads are great for kids, it's like getting them free, I don't know if I buy the canvas, but these artist pads are great, they really are. So that's what I recommend there this week, and here's another one for the Saturday and Sunday door busters, just booster cables, it ends up being five bucks, you get 15 bucks, you get a $10 card, so I think that's it for this week on the odd lot, job lot, and these knives here, they're pretty sharp, if you need a couple chef's knives or stocking stuffers to give somebody, I have one of these at home, they're not the best, I mean they're not heavy duty, the handles are hollow I believe, and it's not as balanced as some of the more expensive knives, but this is a good deal, it's like getting free stocking stuffers, and I'm still interested about this gaming box, I mean I've always been a gamer my whole life, remember when I was younger, but here's something odd this week, we're not really going to go into shop right, because I think they're just sort of, they got their fill, and there's really nothing good this week, there's no real good meats on sale, they have their cheeses, these cheeses are always a good deal every week, so it's no point in pointing them out, so I'm not really going to talk about shop right this week, nothing groundbreaking at all, boring this week I think, so I'm not going to talk about it, but we'll make a brief mention of Walmart, Walmart this is interesting, they have good deals on things like a 40 inch TV at 1080p, they want 4K now, but that's ridiculous, but the thing you need to understand about all these high tech things, look how clean they make that, next year they're going to be obsolete practically, or you're going to want something new, so see if you can do without it, I mean this is a good deal, this gaming laptop seems, I don't know, I would recommend against tech, I mean because it's, tech is bizarre, it doesn't last long, it really truly doesn't last long, and they get you buy all this stuff and you're going to buy the similar thing in a year or two anyway, so it's bizarre, but the thing they do have, and cell phones too, you're going to need a new one in a year or two, it's just to hold off, buy a used one on Amazon, like two-year-old model, you get them really cheap, the thing that that might be good at a place like Walmart this weekend, or toys for the kids, because that you can't avoid the toys, it's almost like tech for kids, all this stuff they're going to destroy it or want new ones, the toys aren't bad and they probably have some decent things on some tools or useful items, so if you could find something you might need, functionally need for the house, there might be some good deals to have, like this Instapot, 59 bucks seems to be the low bar for those things, I mean when they're $29 I might buy one, but so that's it, it's mostly consumer junk, and you know what's the best deals this Black Friday weekend is Lowe's, I mean I'm not sure Home Depot has similar good deals, and I'm not going to get into every deal that Lowe's has here, but they have some incredible deals on things like that used to be really expensive, and this should be the only time like these refrigerators, it was normally $2,200 bucks, $9.99, I mean that's a profound savings, and like around Christmas time these bit kits, like a hundred piece, normally $50 bucks, $17.98, those are really really good deals there, they probably sell out, they probably just have just enough, but all throughout this entire Lowe's Flyer they had really like very low priced items like for instance I like this, these step ladders are extremely useful, $19 bucks, normally $45, and they had another ladder in here that I might pick up, because we don't have a good folding ladder in this house, and if I could find it in here it's worth mentioning, but other than that I mean like if you really look hard you can find some really good deals at Lowe's, I think it was on the back, yeah, this five foot ladder is normally $70, only $22, you cannot beat it, and we have one of these little giant ladders, they're real bulky, but they take up less rooms, they're like four different ladders, you can have four in one, essentially you can have a folding, but I don't use this, so that's why I want to get one of these guys just for quick jobs instead of having to schlep this this thing out, so that's it, I really do think Lowe's has the best Black Friday deals in terms of discount savings on what's useful around the house, so that's it, have a nice Thanksgiving weekend, and I'll see what I can come up with next week.