Oh, it is. It's not bad. It's so juicy. It's so juicy. F**k! Follow us on personal YouTube channels, the description below. Yep. Today we take a little break from our, uh, classic month. Yep. Uh, just, we told you it might happen. Yep. Uh, if something new drops, we would do that. Yep. So, uh, we do have other classic films to get to before this month ends. Yep. So we'll be getting to those. Yep. So don't worry. Yep. If something new drops on Amazon, Tritium? Doast. Yes. Uh, and the, uh, not to be confused with Doast. Uh, what's your name? Um, it's the Malialum, which we have yet to see the original first one. But, for those of you who've been around, we did see the original Hindi. I asked the team, I said, is there a reason to watch the first one outside of just watching it? Is it any different in terms of story than the Hindi? You might say it's a better version, but is there any other information that we'd be missing? They said no. They said no, we could just jump in this one. Which made us get to the review sooner. Yes. Yeah. I forgot my computer. Well, in the meantime, what's funny is I didn't realize it too. Corbin forgets stuff like the pewter. Like the pewter? Yeah. Your pewter. That's what happens after you have all those beans. Anyways. Yes. Adricium II, it's a gripping tale of the investigation of the whole family which is threatened by it. Yeah. You know what else? Basically, it follows the story of the first one. What happened after... I don't know if I want to say it's anybody's... I know. The first one. But you could... I mean, you said it's a gripping tale. Spider Monkeys have gripping tales. That's true. Yeah. But it takes place six years after the events of the last one. We kind of can't go through this without... So if you want to watch it, don't be spoiled. Go watch it. It's on Amazon. It's free if you have a membership. Well, we don't have to... We don't have to spoil it. I'm just saying, you can't really talk about this without knowing... Yeah. We'll try our best. Regardless.  So, Rick, your initial thoughts, please.  I love you. And I just... I will never lie to you. And I will... I'm about to anger a lot of you and I'm very, very sorry, but I would rather be honest with you and love each other than you'd be mad at me and love... I didn't lie. Yeah, I didn't either. And before we get into it, and a bunch of comments say, don't watch Malayalam films you don't understand. This is our 11th. We've loved 10 of them. So... Regardless, I will go over what I did enjoy, but there was more I did not enjoy than I enjoyed. I thought whenever you eventually got there, it was, I guess, seemingly interesting what they... The little twists and turns kind of like at the last one. Mohan, I thought, did a fine job. He didn't really have a ton to work with, I think. But he obviously... He didn't put in a bad performance. I did really enjoy the T-Shop worker. I thought he did really well. I thought... So... Okay, let's take a break for Corbin. Hey, what'd you think of Drisham too? I really liked the T-Shop worker. So here's the thing. Okay. And if you only like reviews that praise what you also like... You came to the wrong place. We're not just going to do that. And I feel like... You might be new here because this is a new film. And you might think we don't know anything. We've seen almost 200 Indian films, 11 Malayalam and all previous to this one I loved. And I thought we're somewhere high artistry, including when they came out this year that I think is the best film of the so far, which is the Great Indian Kitchen. Yeah. I thought the biggest issue with this film that I think if they would have gotten rid of it, it could have been a thousand times better. It was the melodramatic soap opera style of filming and editing. And I just couldn't get past that. I hate that.  And if you don't know what we're talking about, if you've never seen a soap opera, it's overemphasizing people's reactions.  And so I think if they would have eliminated that and just made it a simple shot and stuff like that, I think it could have been a thousand percent better of a film. Because I actually don't think it's actually... I'm acting, of course. But I actually don't think that was the main problem. I don't know if you agree. But I think it was actually mostly the overdramatic editing and score. But behind it, that for some reason they were... I don't know if that's how the first one was, but they were making it very, very melodramatic. And I hate that. I hate it. Just consider us pen and teller right now, guys. Yeah. I'm just nodding in agreement with my partner here. Just I... We don't enjoy doing reviews of films that I've only actually heard praise for. No. Everything we watch, we go in wanting it. It's like, why would you want a movie you're watching to be bad or you don't enjoy it? Every film I ever watch, I'm rooting for it to be good. I'm looking for ways to praise it. I'm even asking myself, where am I imposing certain things on it? I ought not be imposing. And yeah. Is that all that and more? Oh, I know. There's more, but I'm saying the biggest issue. If they would have taken this issue out, it would have been a C-plus film. Yeah. If the soap opera melodrama in every way, shape and form, score, editing, lighting, direction of the actors, everything, it was a soap opera. If that had been changed, that would have dramatically solved half of the problem I had with it. The other half of the problem I had with it was as much as there wasn't anything in the acting that was anything that I found grippingly wonderful. The tea shop worker. The tea shop worker. Yeah. There wasn't anything where I was like, for me, after the soap opera, there are so many things about the story I had. I just, it's beyond. There's a lot of self in expository writing that is just, and I know many of you will probably put in the comments, oh yeah, well, Dressium was the biggest box office success in Malayalam history. Doesn't mean a thing with the artistry. So was Phantom Menace.    And it did box office. It was annoyingly expository in this way. Yeah. Anytime a character has this happen. Have you heard? Yeah. We should be shown that, not told it. Yeah. It's just a basic script writing 101 thing. So by the time, by the time we actually got to the big reveal, which was strained credulity for me. Yeah. And I understand that they said it in the film, it's a film and that's what they were going for. And yes, I think this is better than Phantom Menace. If Phantom Menace was on and this was on, I would be not happy bad and I would watch this. Yeah. Anyways, but yeah, if by the time we actually got to the big reveal, right at the end, I was already so annoyed. I was like, okay, cool. I guess. Yeah.  Or. And I guess he's the only one with a video camera in the entire village. Well, and I was, I was even thinking to myself, okay, is this one of those things where, like we've learned about the judicial system where there's no jury trials and things that we were wondering about with getting evidence and handcuffing people. We've had those questions, right? I just, this, this was like, okay. Well, I do know that like obviously when he, when he confessed to the police officer, right, right. But once again, that's not admissible. Remember, we learned that in crimes. Right. You have to have a, I think it's a magistrate, right? Present if for a quote to be admissible. So obviously he could change his. He did. Yes, obviously. And did his story to make it. And I also think they dragged it out. Obviously, I think it could have been two hours long max. And there was a bunch of information that I understand they did it to show, you know, what he was doing and planning and all that kind of stuff. But it could have been much more brief. And this, this film should have been an hour and a half to two hours max. Yeah. And it also doesn't help that we're watching this after I'm in the thick of watching some of the best cinema on the planet right now from all over the world. And that, and by comparison, have come out of seeing things that are in the running for all of the awards internationally from France and from Spain and from Russia and from Chile and from, I, this was just really, really hard in that regard. And I found it really, even at the end, I don't understand why the parents felt it was a greater punishment for him to live freely with guilt than it would be for him to pay for his crimes because he gave them the DNA. He gave them the dead body at the end. I think it was cremated at the time. Yeah, but still. Well, I don't think you can get DNA out of cremation. Well, no, but I mean, here's the remains. He's admitting it again. And there's the cop again. But he could just say that's not his, that's what. Yeah. I understand. There was a lot of strange credulity. Just strange credulity. And the whole climax. And I understand they explained that, that the hero needs a bit of luck. But I didn't really like that whole thing, that this whole thing was a film. So, we didn't like it. Once again, I don't like doing these reviews in terms of ones that I just, I don't like the film. Especially when all of you love it, like that airplane movie, the Tamil film that we hated. Right. I understand this will probably get more dislikes than likes. I get it. Oh, there will be people who just love him, and they will be very angry that we don't get it. Yeah. Okay. I've loved every other Malayalam. I think we've had, Kumbhavati Nights might be the best Indian film I've ever seen. Like every other Malayalam. Well, and didn't we see the other one with him and we liked him? Yeah. We've seen one other film. We've seen one other film. The face dancing. That was our favorite thing about the film was him. And then he didn't do anything. I agree with you. He didn't do anything bad. No. But it was just, I didn't feel like there was much for him in the script to go with anywhere necessarily. He just, he did what was asked of him to do on the page. Yeah. I felt it. So, once again, I could harp on a lot of this film, and I just, I don't want to.  So, yeah. That's what we thought about it and we're going to be honest. And very, you know, it's very, want to be honest and get aggravated about things, especially when there's things that are blaring for you. But I also know filmmakers, they don't go out of their way and wake up and go, hey, let's show up to set today and make a bad movie. Let's just do everything we can. And from script to the end of it, let's just do, that everybody's out to try and do their best and do whatever they can to do what they're going to do. And it, for me, like you, this one just didn't flip the boat by any stretch of the imagination. Once again, we love Mali Alam. We do. We love Mohanl. We want to see, in fact, before we're watching this, we were going to watch a classic Mali Alam and we still might. And I believe it had Mohanl in it. But let us know what's the next Mali Alam cinema we should watch. Let us know why we're idiots. Idiots. I'm sure you will. Hatred's coming. And unsubscribe if you want. Yep. Let us know down below.


Hi, how are you? I hope you're doing well. My name is Ndanya and welcome to S-Prembers. Today we are here on location at the Tamarind Hotel for Mental Health Summit. We are here to talk about the increasing amount of mental health cases. Majorly we're gonna be prioritizing people with disability and other special cases. So stay tuned at S-Prembers for real-time updates. Various NGOs are here to give more guidance and they just tell us about mental health. So you said I should say what my neighbors' expectations are. Which one? Whichever you choose. So I'm going to say why the immediate person who just spoke his expectations are, he wants to understand why it is actually frowned upon for men to cry or expose their feelings and it is thumbed as a weakness and I'm also very curious about that. So yeah, your name and where you're coming from. My name is Tracy Likoko, I'm from St. Paul's University. It's a lot of representation from St. Paul's. How many are from St. Paul's? I'm nine. Okay, so I can pick someone who's done from St. Paul's to say something. Good morning. Good morning. I'm Karan Jutwai from ICMili Money. My expectation is, we are mostly faced with this challenge of mental health so I'd like just to know more about mental health so that I can be able to help my friends and myself as well. Okay, great. What's the message? What's your neighbors' expectations are? Good morning. Good morning. I'm John Wakami. So my neighbor's expectation, I'm from Kwae. My neighbor's expectation is to get an outlook on mental health is to get like that psychosocial support that you need, the emotional support that you need when you face maybe depression and other issues that people face through life. Thank you. What's your neighbor's expectation? Good morning. Good morning. Whoever you spoke to. Good morning. I'm Faith Mdina from Kwae. My neighbor's expectation is to learn to learn about wider perspective of mental health. I'm Tonya from Kwae. So my neighbor, he expects to get to understand himself better because he believes when you start understanding yourself that's when you'll get to understand others and expect to learn a lot better. Okay, round of applause for her. So there's a lot of people expecting different things and that is beautiful because we're here to talk about matters mental health and for sure you will be equipped to understand mental health better. You'll be equipped to also know why men are told or maybe they don't cry. I would want to know that also. You'll get to understand how to deal with mental health issues, your personal issues and I'm sure that once we are done there'll be growth. There'll be enlightenment. We will have something to look back and say I learned when I attended Peat Stop. Yes? Great. So I want us to fast start with a word of prayer. Is that okay? Great. Can I ask a volunteer? We have a variety of people represented here. If we can have someone to start us off with a word of prayer. Just thank God for being here. Thank God for this opportunity standing here, being alive. Anyone? I can peek. Kindly. Tell us your name and where you're coming from and then pray for us. So hi everyone. My name is Ashli Akot. I'm from Saint Paul's University. So let's believe. Dear God. Yes? So still I rise. That is just me sharing an aspect but there is something, there's a theme that we have today that we are carrying with us today and it is this world is. Let me stand next to my boss lady to tell us the amazing thing that she said for this wonderful two days. This world is possible. This world is possible. Do you agree with me? And I just want you to take a minute and time to the person next to you. When you think of that theme this world is possible. What does it mean? What is possible to you? For a minute. What is possible to you? Ngobi, what is possible to you? When you think about it this world is possible. It's possible. Anyone, chef? When you say this world is possible what do you think? When you say the world is possible I mean but I can do anything that my mind thinks of I have that capability to achieve anything that my thoughts can think about. So you can achieve anything you set your mind to do. It reminds me of a quote that whatever the mind is in the heart conceives and believes you will achieve. So same concept, yes? Great. What is possible? Possible is certainly possible comes in a lot of ways I cannot prospectively say everything but possible is different to you and to me so what is possible for you what is possible for me but then again in general every single thing you put your eyes to you set your eyes to make an effort to do is possible because it's all in the mind. It's all in the mind. Everything is possible depending on how you interpret that possibility. What is possible? What is possible to you? Possible to me means obviously something that I put my mind into and once I work it out in my mind that means I can be able to achieve it. There's a lot of alluding to the mind and it's interesting because you're talking about mental health because this is where it all starts and this is where the limitations how many are. Am I right? So when you think about it and this I'm going to pose a rather difficult question what has been the most impossible thing for you to do and why? Don't overthink it. Don't overthink it. Is there anyone who's vulnerable enough to share what is that thing that you've considered impossible to do for yourself? Like I just can't do this. There's a volunteer guys. I think the aspect of weekly and the fact that I can be so emotional that I cannot control or rather the busy speak to myself the power, the energy that I can give to be able to perhaps speak to someone else from their feeling so low it's quite different from the other end because I feel like the other end somebody has to do it for me they have to speak it to me so that I get to feel the way I speak to them. So if I understand you you find it rather impossible to speak to yourself so you want someone to speak to you to affirm you. It's easier when someone affirms you than you affirming yourself. How many relate to that statement? Okay. A number of you. Okay. I do. Someone else who wants to share that thing that they find there you go. Thank you. So I think for me it's been believing in myself enough not thinking that I am enough because most of the time it's always going to be what if it mess up what if it doesn't work out the way you expected it to work out so I think for me believing in myself enough to know that I can do it. Believing in yourself enough to know that you can do it. Anyone else perhaps from this amazing area of speakers that we have anything that you considered impossible in this world that we see things are possible. Money is a bit interesting because it has to do with my life I've lived in a life where I've done plenty and I've lived in a life where I've not and one thing that's come out in everything that I've found it impossible for me to give up on my life that when I was at the top of the mountain and enjoyed it and when I've been in the bottom of the body I've always looked up to the top of the mountain and tried to figure out how to get back to the top. Wow. I like that when he was done was looking up which had he, do we ever do? In fact many of us when we were down we beat ourselves even more. So that was just to show you that we are all human, aren't we? We all go through times where we see impossibilities but if you look deep within you can actually overcome it. It is possible for you to affirm yourself it is possible for you to overcome whichever challenge that is thrown at you It just depends what lenses you're looking through So allow me to start us off by saying that this is going to be a very candid kind of meeting We're going to remove our masks and we're going to share bare naked and unashamed It's going to be that meeting that we're not going to pretend because you're saying it's okay not to be okay It's okay not to be okay Ya It is okay to hurt and not be able to articulate it because all you can do is shed tears and bowl This is that kind of meeting where our speakers will pour their hearts out to you so that you come to the understanding that no matter how difficult no matter how bleak it seems there's always light at the end of the tunnel and we are here to affirm that over and over again there is light at the end of the tunnel To start us off this morning is a friend whom I have known My sister, the first one will be better than the house How cool is that? I miss those days but first forward I love what can be asked What is that thing you are afraid to do She mentioned Kid Stop I stand here today as a testimony to all of you All my siblings and those who are my friends know that my Nikle was home alone I was that person who was always at home I would never talk to people when visitors would come I would refuse to go and say hello to them and when I would be forced to greet them I would turn off the light and pretend I was asleep That's how shy I was but God had a message and a testimony and a purpose for my life So first forward to me starting working and over days when I didn't believe in myself and I remember I started out doing sales and I was there like What does sales require? Talking to people Who's the next part in talking to people? Thank you But again God has a sense of humor and so I grew and in that process I began discovering certain skills that I had I'm a creative at heart and everything in my So how does mental health look like where we are A study was done in 1986 by the Center for Disease Control and the study was called Adverse Childhood Experiences What we call 3 Realms of Assess and you say that if these things happen to you between the ages of 0 to 18 they increase your stress level and they reduce your resilience capacity to withstand other issues especially as you age Okay Adversities are found first of all within the household and one of them is emotional and sexual abuse The other one is alcoholism and drug abuse if you live in a house that has alcohol and drug abuse if you live or come from a family that has a parent who has a mental illness or even a parent who has passed away or is absent but present the speakers will talk about this more if you come from a homeless home if you come from a family that is divorced if you


Hi, good morning and welcome to today's products and focus so global markets had a bit of a tough session yesterday having rallied Later on in the session it dipped that down towards the very very end and actually from a technical analysis perspective This is a pretty ugly candle to get on the US 30 now. We've had a bounce this morning, but it's below 17 747 So looking at the tips of these candles and what we had yesterday the from a technical perspective The pressure is certainly on with a crossover the MACD a cell signal on the RSI and the slow stochastic We've got 17 561 is the next potential support. We should also break the back of the 21 period SMA So then looking at the UK 100 a similar ugly picture Trinium below potential support coming up quite close to the 55 period SMA with 6073 be the next potential support But obviously we're far away from there right now 6300 is potential resistance at this time then jumping on to the Japan 225. It's still kind of slowly grounding higher We'll have a look at dollar yen in a second But it's still all about if Japan are going to embark on quantitative easing or not But 20,087 is a potential resistance to be aware of so looking at dollar yen It's struggled as in the US dollar has has kind of lost its momentum slightly But the major fundamental factor hasn't changed that it could be a rate hike in December to be fair It's just in the absence of MACD data The dollar is not really advancing the way that it could With some extra evidence to back up its view, but lots of central bankers speaking today you've got a number of Fed members speaking today including Yellen and A few other Fed members throughout the end of the day and that could have a slight impact there may be a kind of medium range Updates so with middle of two ranges 121 spot 87 and support 124 spot 42 as potential resistance So moving on to West Texas crude it was a pretty bad day again yesterday This is slowly grinding towards $42. It's not stone throw away from there right now Things get a little more interesting West Texas crude if you break below 42 and that's not happened as of yet So far it's been oscillating in this range between 49 40 and 42 dollars Then moving on to gold gold is it back in the slide again a 1,000 72 dollars in the potential support 1,100 Excuse me As potential resistance, but we're a good bit away from there all technical indicators are pretty much showing that this is oversold right now But the the yellow metal certainly under pressure at the moment finishing up with GBP US Do you have your dollar in GBP USD so your dollars are traced back up to one spot 0 786 is a dollar taking about the back seat This is a very interesting level. It's bounced off here a couple quite a few times So depending on your view, this could be an interesting strategic point The other technicals are quite overbought as oversold as well. So that's one thing to consider. I'm finishing up with GBP USD Sterling managed to break up back through one spot 51 85. That's quite impressive actually And we are at the right on the right side of this So this could be a springboard if you are bullish on the sterling to get up to one spot 54 24 Or if you think that this is This could turn itself around from a technical from a candlestick Aspect obviously we're still in the middle of a trading day. This is very bullish. Okay, so finish the top end of this range This is a graveyard doge information. It's not even remotely closed yet But it's trying to push higher and has been pushed right back down again. So depending on your view If we go back down below one spot 51 85 That's when things get a little bit more techy for GBP USD again But for right now it's on the right side of potential resistance So it could go that little bit higher depending on how the macro data system comes out So I come at data-wise. We've already had a CPI from from Germany Pretty boring to be honest Then we've got industrial production in the Eurozone employment claims and of course weekly petroleum crude oil inventories Which is now falling on a Thursday currently and this is a big one for West Texas crude today So don't forget to set your alarm for that if you are a crude trader lots of good opportunities there we think So looking at tomorrow. We have GDP for Germany GDP for the Eurozone trade balance data as well PPI US retail sales US and the consumer sentiment survey University of Michigan Data so actually Friday comes with it Opportunity for the week to finish with a bit of a bang because quite a lot of US data all high level red important level impact stuff there So make sure you don't miss out on that. So I Can see here. There's some good good quite interesting analysis from our Team in the UK on the chart form. So some UK 100 copper Dollar yen you're sterling get a chance to see that make sure insights are part of you later going forward and join me again Tomorrow to find out what happened next


In the Guild and also in the university alliances you know we're talking about research strong universities so in civis we have several hubs that address relevant issues like climate or health or societal issues and link that to the design of the mobilities. I Think you know and maybe this is taking it a little bit a step too soon because it's a point We're coming to but I guess we need to explore that Deeper is no matter what the design of the mobility is. I think we it should Link to previous experiences. I mean young you know that I'm very much a fan of John Dewey And I still think that he was very right when he said that experience has to build on each other there has to be a continuity and there has to be a extensive and intensive growth Which relates both to the subject matter to the content we teach But also you know to the social and emotional experiences the students have and I think we have to have all of these Dimensions in mind and then think you know how does that particular program link To other activities which the students had to other situations they were in so that there is you know There's these two principles of continuity and interaction Both have to be present no matter whether it's physical mobility or virtual mobility or blended our students and their voice Is really part of this co-creation But we're talking about and we take for granted resilience and we're taking for granted mental health Well-being and strategies in place and students who can cope with the type of educational experiences that would require them to spend Six months Warwick six months to begin a back at Warwick Then back to begin and then go somewhere globally and so on these are not the students I see in many times when I work with my students when I work with students in other institutions where I work with students In other institutions across the world. So there are issues that have been exacerbated that actually something like this would be detrimental We would have students dropping out. We would have add us adding on to the anxiety as adding on On on sort of conditions that are there it takes time for our students to settle in and so on so we often talk also having a sort of Probably different generation of student in mind with sometimes is makes me think is it that we come together and we design and sort of the engagement with the students not as deep as as it should be because What does opportunity mean for whom is fundamental? Yeah, and can I just when you say supportive structures? I think it's important to warn. This is not Psychological support. I think if we look to the North America, they are I just heard reason is more and more psychologist is that this at the same time the degree of Not feeling well is increasing. So it's not providing each person with their own psychologist on the contrary. It's meaningful Engagement from my point of view. I see the solution in what I call semi joint degrees so instead of really demanding a European degree with the very tight integration between and so in the Planned way that you have to spend. I don't know four semesters in four different universities in order to get a European degree and finally you have this bureaucratic in a sense that that we have been interviewing the joint degree Program managers in our universities and also elsewhere and asking whether there is a benefit of this European degree and the general answer is that That the University academics don't see the benefit the students at least in Europe don't see the benefit and the employers don't see the benefit Then maybe the outside of Europe the students who are coming from outside of Europe They see the value of the European label on the degree But but instead of this kind of organization, which is very expensive It's very it can be done with a very high quality and if it's supported with Erasmus Mundus money It can be organized with a high scholarships very good students and the students who want to have this kind of and who are ready for that And who's mental healthy who are mentally happy of moving from one country to another and having Who see this as an opportunity to also engage in the different labor markets and to see the different labor markets But but that's really we see that it's a very limited number of students currently available


Welcome back. Today, we will discuss a very important concept, the concept of independence of random variables. You will recall that we have already studied independence of events right and we have also studied independence of sigma algebras. Now, independence of random variables, so in elementary treatment of probabilities, so you might have studied in your under grad, you would have studied independence of events and independence of random variables and you get two different definitions right. What we will do is we will adopt an approach, which brings independence of random variables and independence of events independent of sigma algebras all within the same intellectual framework. So, I will define independence of random variables in terms of the independence of the sigma algebras generated by the random variables and then later we will verify that the definition I am going to give is consistent with the more elementary definition of independence that you are familiar with. So, recall that, so as usual this is the picture, so you have some omega f p and let us say you have two random variables x and y that map elementary outcomes to R 2. This is the picture we have and we said that for any Borel set B in R 2 we can speak of its probability law, its probability that the pair maps into that Borel set right. Also recall that, we defined sigma algebras generated by random variables as follows in particular we said sigma algebras generated by x as the set of all A's subsets of omega of the form A equal to x inverse B for some B in B of R right. And similarly for sigma y, sigma y will be you call it something set of all call it C in omega that is that C is equal to y inverse B for B in B of R. So, these sigma algebras, so the sigma algebras sigma x is consist of all those events here whose outcome is completely determined by the realization of x. In particular every event in sigma x is of the form set of omega for which x of omega belongs to B and similarly every event in sigma y is of the form set of omega for which y of omega belongs to some Borel set right. It means, so far now definition, x and y are random variables on omega f p random variables x and y are said to be independent if sigma x and sigma y are independent sigma algebras. So, this is the definition we will take. So, as you can already see I have defined independence of random variables to random variables x and y in terms of independence of sigma algebras which is something we understand already. After all independence of sigma algebras just corresponds to independence of events right. If you pick one from here and pick one from here they should be independent events correct. So, this definition brings independence of random variables sigma algebras events everything in the same framework. So, in other words for any Borel sets B 1 B 2 in B over we have probability of omega. So, let me write this we have that the events omega such that x of omega belongs to B 1 and omega such that y of omega belongs to B 2 are independent is that clear. So, I defined. So, I said x and y are independent random variables if the sigma algebras generated by them are independent sigma algebras right. What do you mean by independence of let us call this f 1 and let us call this f 2 right. So, they are all sub sigma algebras of f right and the probability measure is defined on these guys also right. So, under this measure p we are saying that these 2 sigma algebras are independent sigma algebras which means you pick any whichever set you want from this sigma algebras and any whichever event you want from this one they must be independent events is that clear. However, so events in sigma x are precisely those which are pre measures of Borel sets under x and similarly events here are pre measures of Borel sets under y right which is what I am considering right. This is the pre measure of some Borel set B 1 under x this is the pre measure of Borel set B 2 under y and for any 2 such Borel sets the events x of omega belong to B 1 and y of omega belong to B 2 must be independent events right under this measure p thus. So, I can say i e actually i e p x belongs to B 1 I am going to abuse notation from the 1 y belongs to B 2 is equal to p x belongs to B 1 times p y belongs to B 2 for all B 1 B 2 in R right this is for any Borel sets B 1 B 2 in R B B R is this clear. So, you can I mean this is we can take this also as the definition I mean this is this is the same as saying this right. So, where any 2 sets any 2 Borel sets B 1 and B 2 probability that x belongs to Borel set B 1 y belongs to Borel set B 2 this these 2 events are independent. So, the it products out like this this should be true for every Borel set B 1 and B 2 are there any questions. So, now what is the next step what do I often do. So, once I make a statement for Borel set I will make that statement for generating class right. In particular if x and y are independent random variables we have probability that. So, I am going to apply. So, I am going to take B 1 as minus infinity x and B 2 as minus infinity y the generating class of the Borel sigma algebra. So, I can I will simply write this as probability that x less than or equal to little x y less than or equal to little y in all this I mean omega sets that. So, that is I mean I am not writing that again and again. So, that is equal to probability of x less than or equal to little x times probability y less than or equal to little y for all x y in R. Now, what is this this is the joint CDF correct and this is the product of the marginal CDFs right I E f x y of x comma y is equal to f x of x f y of y for all x y in R. So, if x and y are random variables which are independent then the joint CDF is given by the product of the marginal CDFs correct. Now, this is the definition that you are familiar with is it not how do you define independent random variables in more elementary treatments you say the x and y are independent if the joint CDF factorizes into product of the marginals. However, that is not quite what I said right I define independence in this way independence of sigma algebra from that I wrote down this Borel set condition and then I said. So, this should be true for all Borel sets right then I said in particular if Borel sets are semi infinite intervals this must hold right. So, according to my definition here this holds, but now you have to prove the I mean from if you if you think that well the elementary definition that saying that x and y are independent if this holds will not be a complete definition if the converse were not true right I mean if this were to hold is it true that this definition holds is it true in particular that for all Borel sets this holds understand the see if you if this definition and the elementary definition are indeed equivalent one must imply the other correct. So, what I am saying is the definition I have given here implies the elementary definition that you are familiar with. However, is it true that the elementary definition implies our current definition I only know this for see this only means that the probability on the probability law over the pi system products out correct it may not hold for all Borel sets right you have to prove it. So, that something you have to prove. So, theorem x and y are independent if and only if f x y of x comma y is equal to f x of x f y of y for all x comma y in R. So, one direction we have already proved in this if and only if right. So, if I write if and only if right which part have a proven if x and y are independent then this holds I have proved right it means I have proved that bit only if has been proved right yes I have to prove the if part which means that if this is given to me I need to prove x and y are independent in the sense that sigma x and sigma y are independent sigma algebra which is the same as saying this holds right for all Borel sets right. So, this requires a proof. So, the proof this proof again I will not do in proper detail I will only say that. So, I already stated this theorem on pi systems right that if you specify a probability measure on a pi system it gets uniquely specified on the sigma algebra generated by it. Then you can also show that if on a pi system the probability measure products out on the pi system then it has to product out on the sigma algebra that is also something you can show. And that is how this comes out right all I am saying is on the pi system of minus infinity x minus infinity y the probability measure is independent right. And then you have by the lemma that I just stated you can prove that it translates to the entire Borel sigma algebra or you can also approach it using caratheodory there is also another approach to this to the if part using caratheodory. So, this follows from. So, if part follows from the following property of pi systems if g and h are independent pi systems on omega sigma g and sigma well this is not what I really want to say. So, let me just let us see sigma g and sigma h are. So, in this case pi system will be the set of all omega for which x is less than or equal to little x. And here h will be set of all omega for which y is less than or equal to little y. And sigma g will be sigma x sigma algebra generated by g. So, and you have for what this condition implies is that g and h are independent pi systems right. I mean this is exactly the same as saying if g is the pi system of x of omega less than or equal to x and h is the pi system of y of omega less than or equal to y these 2 are independent pi systems big by this. Then from this you can prove I mean this is a property you have to prove from which this will follow. It requires a proof, but this you can see the proof is there in Williams if you want. So, is this clear. So, it appears that I am complicating things right you may you may just be very very happy with this definition this says the definition right. But actually you can take this as the definition it is equivalent once you prove this result you can take this as the concept of independence. The reason I do this as I said I mean all in more advance treatment you always look at independence of random variables as independence of the sigma algebra generate. And it is actually a more elegant treatment it may be a little bit hard to digest in the beginning, but the nice thing is independent of events and independence of random variables come into the same framework. They are not like disparate concepts right. In fact, the independence of events also can be define in terms of independence of random variables right. Now, what we did is we define independence of events define independence of sigma algebras then we define independence of random variables in terms of independence of sigma algebras. You can also do the opposite you can just say that x and y are independent is same as saying sigma x and sigma y are independent. Then say events a and b are independent if the corresponding indicator random variables are independent if a and b are independent if i a and i b are independent random variables. So, it is all within the same framework now you can actually prove that they are equivalent i a and i b are independent random variables if and only if a and b are independent events that you can show as an exercise. So, even if you never define independence of events you can go the other way as well that is what I am saying right. So, it is all in the same framework is there any questions on this is this clear to everyone. Now, how about if you have more than two random variables the same story right the same you can just give the same definition now right. So, shall I just give for n random variables and then state for arbitrary random variables. So, let so definition again. So, all these random variables x 1 through x n live on omega f p they all live on the same probability space random variables x 1 x 2 dot x n are said to be independent if sigma x 1 sigma x 2 dot dot dot sigma x n are independent sigma algebras. So, this is to be understood the same way. So, you pick any event here any event here. So, one you will end up with n events n boral sets and you should have independence among them right and actually there is no sanctity in taking only n of them you can take any arbitrary collection of random variables and define it in terms of I can define it in terms of the independence of the corresponding collection of sigma algebras right. So, so far you will be. So, you would have seen this in elementary treatments you will say that x 1 x 2 x n are independent random variables if the joint c d f of all of these guys products out into the individual marginals that you would have seen right. Now, I am going to say something a little more I am going to say definition a family of random variables family x i such that i belongs to some indexed i of random variables is said to be independent if the family of sigma algebras sigma x i i well sigma x i i belongs to i is independent. So, you have a collection of is a family of random variables this family of random variables may be in infinite family actually this can be even an uncountable family of random variables this i can be index by any set you want any arbitrary index set and in that case you say x i are independent random variables if the sigma algebras generated by each of those random variables. So, this is what kind of a thing this is a family of sigma algebras and we already know what it means to talk about independence of a family of sigma algebras right we I think we gave the definition right. So, what does that mean? So, you call this f i I think we use f i for. So, a family f i of sigma algebras is independent if you pick any event you want from each of these guys that must that family of events must be independent. So, that is something we already understand right now if you want to write down a c d of definition for this is a bit of a headache right. So, here you can do it right. So, this is a very elegant way of treating the whole matter and you give me any collection of random variables I define it to be independent collection of random variables if the corresponding collection of sigma algebras that they generate is independent sigma algebras right they are independent sigma algebras. So, it gives a certain aesthetic I mean it is kind of in the same framework right you do not have to give a different definitions for finite family infinite family this that right you can just finish it in once you know what independence of sigma algebras is you can just finish it in one frame work. Is there any questions. So, in effect what this means intuitively right I mean this is a definition that you understand in terms of the earlier definition, but. So, what this means is that. So, recall that sigma x i is collection of all events here whose occurrence or non occurrence is completely decided by the realization of x i right. So, what I am saying here is by saying this sigma algebras are independent I am saying that. So, you cannot decide by. So, what you can decide by looking at x i the set of all events you can decide by looking at just x i and the set of all events you can decide by looking at the x j s realization those events are independent right that is what this means correct just take it for x y if you are confused if you take x. So, I am saying that the set of all events whose occurrence or non occurrence is decided by looking at x and the set of all events whose occurrence or non occurrence whose is decided by looking at y those events are independent that is what it is ultimately saying right. So, if you want to say it very colloquially you can say that oh looking at x I cannot really figure out much about y right, but that it is a little bit I do not want to make such a lose statement, but that is roughly what it means right the set of all events you can decide by looking at x and the set of all events you can decide by looking at y are independent events correct. So, we can. So, if you adopt this line of definition you can completely avoid the CDF definition right any questions no more questions I will move on to the next topic. So, you take some time to digest this it is a very powerful way of looking at independence you may resist it in the beginning a little bit because this the CDF definition seems over so much more familiar, but this is actually a more powerful and more general way of looking at it and it is mathematically equivalent as we know right. So, I am going to switch gears completely now I am going to. So, we study these types of random variables right. So, for single random variables we said x. So, if you have a single random variable x it is categorized differently based on the nature of the measure p x induced on R right and we said it has to be one of three fundamental types or mixtures thereof discrete continuous and singular right. Now, we are going to look at let us say for just for two random variables what the possibilities are right actually there are lot of crazy possibilities right along one axis you can have one the other axis you can have another or some crazy mixtures thereof right, but again the interesting cases. So, we will not worry about singular as I said right. So, the interesting cases only correspond to so x and y being discrete x and y being continuous so on right. So, some nice cases what we will study in those nice cases for example, when the x and y are discrete we will talk about a joint PMF and then we will talk about conditional PMF. Similarly, we will say that if x and y are both continuous random variables it may not be the case that x y is jointly continuous. So, these are concepts that we will study. So, in the sense that so in the discrete case it is easy right if x and y are both discrete random variables it means that with probability one they take countable values which means the pair x y is taking countable values clearly with probability one that is the simplest case of the case when they are both discrete. But the case when they are both continuous if x and y are both continuous it may not be the case that the measure induced on R 2 is necessarily a continuous measure right some that is not a very easy case. So, that so it that requires a definition of joint continuous random variables those concepts you will get to know. The easiest of course as I said this discrete random variables. So, this is the case of so if discrete random variables you take two discrete random variables x and y living on the same probability space. Now, so this you are looking at a measure on. So, you are saying that x takes only countable values with probability one and y takes countable values with probability one. Now, if you look at the map on R 2 right what happens. So, you will you have so on. So, x so this let us say this guy is x this guy is y and we know that x being discrete it will only take countable set of values and y also being discrete will take some other discrete set of values. Which means as a pair x comma y the values they take will be the simply the Cartesian product correct. So, if I mark the points with x. So, I will get all these points right. So, I will simply get all these points right and so on. So, you see that and you also know that if you take two countable sets and take Cartesian product you will have a countable set again right. That is a I think that is something we did not prove, but it is true. So, if you have a countable set like this right. So, you have one countable set like that and another countable set like that the Cartesian product can be can be it is like you can count it like that. You can arrange a if you if you go like this you may never finish to come here. So, but if you count like that you will get a arrangement. So, you can show that Cartesian products of two countable sets are it is a countable set. So, the range on R 2 will also be countable with probability 1. So, on R 2 the measure all the measure is sitting on some countable set on R 2 all right. So, essentially if x and what I have said is that if x and y are discrete the joint measure is also sitting on a countable set. So, x and y are automatically jointly discrete this we may not appreciate so much now, but I am going to tell you that if x and y are separately continuous x y may not be jointly continuous. So, I can speak of a joint P M F which is defined as P x comma y of x comma y equal to the probability that x is equal to little x comma y equal to little y. This is called joint P M F and this is defined for all values of little x and little y. However, it will be non-zero only on a countable set in particular this will be non-zero on the Cartesian product of e 1 and e 2 where the e 1 and e 2 are the countable values that x and y take. And again just like in the one dimensional case if you give me the joint P M F of these two discrete random variables I can figure out the probability law for any Borel set on R 2 how will I do that. So, you give me whatever Borel set you want on R 2 let us say it is that that is your Borel set what I will do I will simply add the P M F of those points in B. So, what I can do is for the so if you ask me for the joint law of some Borel set B. So, let us say B is in B over 2 I will simply write this as the summation over little x little y in B P of x is equal to x y is equal to y. And so I mean this will only be non-zero on those points right where I mean it will only be 0 on the Cartesian product of the two ranges of x and y. So, why is this true by the way yeah it is countable relativity right because this B. So, the measure of B is simply it is measure is 0 outside these points of these points the measure is 0. So, it is measure is given by the addition of the measures of these single terms right everywhere else the measure is 0. So, this way so let me just say this is non-zero only on a countable subset of R 2. So, if just like on one dimension or two dimensions if you give me the joint P M F I can figure out everything there is to figure out about random variables x and y discrete random variables x and y. Any questions yes no I will get to independence soon. So, I am just talking about. So, I have switched here completely. So, I am just talking about I finished independence and defining everything about independence I am talking about now x and y both being discrete right. And I am saying that joint P M F is enough to characterize the joint law and if I know joint law I know joint CDF right. So, next definition let x and y be discrete random variables on omega F P. The conditional P M F of x given y equal to y is defined as probability of x is equal to x given y is equal to little y which is equal to little p x comma y.  So, this is defined by divided by p y of y where p y of y greater than 0. So, this defines the concept of a conditional probability mass function conditional P M F. So, what you do here is you are given two discrete random variables and you are fixing the value of y. Let us say this little y is one of the values that capital Y takes with positive probability otherwise you cannot condition on it right. So, you condition on y equal to y and look at the probability mass function. So, how is x distributed given y is equal to y that is given by probability obviously this is given by the intersection of this and that which is your joint P M F over probability of this guy probability of b which is. So, it is a very obvious definition. So, intuitively what it does is maybe I can just go back to this figure just clean it up a bit. So, if you just look at I am conditioning on y equal to y right. So, let me say this is the y I am conditioning on. So, I am fixing the y. So, if I fix a y I look at all the values of x it takes and I simply. So, for each x I define the conditional P M F as the joint P M F scaled down by the probability of y equal to y. So, I am fixing y equal to y and I am in some sense scaling these masses to make it a you make it a valid probability right. So, you mean after all if you sum this over various x's you will get 1 right. That is what is intuitively happening if you sum it over all x you will get 1 right. So, in a sense you are fixing a y and you looking at what x is distributed as this is a picture you are scaling all these masses to make it a valid P M F and it is a P M F over x and depends on which y you fix all right. This is definition clear any questions of this definition. It is actually I mean fairly elementary right this we. So, in the case of in the continuous case singular case and all this gets messy because you can know it is not you cannot really condition on a singleton right it has 0 probability. But, in discrete case there is no problem this is very elementary. So, we will. So, we have defined this conditional P M F now we will move on to characterizing discrete random variables and looking at independence of discrete random variables. You can get some characterization in terms of the P M F's and conditional P M F's for independent discrete random variables which we will do next class.


This is EFNN the tiger financial news network Good Monday morning everybody I'm Tommy O'Brien coming to you live from TFNN 10 a.m. Eastern Time Monday 30 minutes into the trading week and we got markets Clawing the losses back and just like that. We're in green by one point in the S&Ps We're a solid 24 points off of the lows we were trading at coming into the opening bell get the NASDAQ 100 We're up by eight points right now. That's a lift of almost 100 points from where you were trading just at about 9 a.m. This morning Dow the only index still in the red by about 45 in the Russell How about the Russell man? You're up by more than a percent from where you were trading at 1780 coming into 9 o'clock. You're pushing 1800 in the Russell you jump over to Bitcoin down about 1.3 percent off $350 $26,195 the crude contract back above 90 bucks trading at 89 80 gold contract this morning Down a dollar at 1944. What do we have folks? We've got lower price on the yields on the bonds Excuse me. We're talking about a 10 year above 4.5 percent again That's up about seven basis points right now the 10 year at 4.5 13 to be exact You got the 30 year up 10 basis points up a tenth of a percent 4.6 21 right now So you have higher yield on a longer term basis, especially that putting a bid into the dollar index We almost just got to a 106 price point on the dollar. We're up by 29 pennies at 105 87 and the dollar index So what do we got? We got higher yield you got dollar strength that was weighing on the market a little bit But we've got a little bit of a bid all the markets basically near flat right now We will see where we go from there And what do we got folks? We got a deal potentially with the Hollywood writers The one thing I will say on this is that they haven't announced the details. Okay, so it'll be interesting to see the details They've said it's an exceptional deal But the devil is in the details. We'll see where they go Disney shares flat this morning so far Netflix catches a bid by about three-quarters percent paramount Basically negative by three tenths percent Warner Brothers Discovery would check in down about nine tenths percent We check in on the other strike Ford Flat this morning. We jump over to GM shares down about two tenths percent Strikes across the board markets back in the red the day is young and we got a treat folks We got a man Larry Pezzavento He is coming up live for our man Basil Chapman Basil's out today forgot about that one But we got live programming Larry Pezzavento. He's in the chair. He's getting ready. He's coming up next folks Have a great Monday. Stay tuned for Larry


Did you ever consider that future human civilizations traveled back in time to reshape history? How would you know? Is it possible that history is constantly being altered and the consequences to this is that we shall never know till we reach the level of understanding hundreds of thousands of years into the future? In 1905, Einstein changed the course of history with his publication that space and time are one and his theory of relativity. How did he come up with this idea? According to Einstein, the idea suddenly came to him in a surreal moment while staring at a street lamp. Is it possible he was somehow given this idea deliberately? Einstein realized that if you move faster, the ticks on your clock actually change. Prior to Einstein, no one understood that or would have even expected that because it only happens when you get very, very close to the speed of light. Think about this for a minute. There is a way within the laws of physics to travel long distances and still be alive and that actually is related to special relativity and the idea that if you can travel close to the speed of light, time will slow down for you. In this sense, if you can travel very near the speed of light, only a day or two would pass for you compared to years elapsing on the earth for everyone else. You can see the future in exchange for your present. Would it be worth it? Wait till you hear this. What if you could travel back in time through an interdimensional space time portal? What if we could influence not only past events, but see how the future evolves? Many believe there are answers that can be found in the ancient Indian epic text. Within the sacred Indian text, thought to have been written around the 8th century BC. King Ravata is described as traveling to the heavens to meet with the creator god Brahma only to return to earth hundreds of years in the future. Some researchers believe this Hindu tale may be one of the oldest records of successful time travel in the ancient past. But how is that possible? The story goes that King Ravata is taken into space to see the gods. And when he returns to the earth, he finds that many ages have gone by. In fact, hundreds of years have elapsed on the earth. This is the kind of thing that would happen to space travelers and in time travel. You think you are gone for only a few days, but when you return to earth, you find out that you have been gone for hundreds of years. Doesn't that just blow your mind? Other tales of time travel can be found all around the ancient world. In Japan, the legend of Urashima Taru details a fisherman's visit to the protector god of the sea in an underwater palace for what seemed like only three days. But when he returns to his fishing village, he finds that it's been 300 years that he has been gone. His house is in ruins, derelict. The way he knew is long dead. No one remembers him or his family. He simply vanished and reappeared hundreds of years later. Could Urashima have traveled through some sort of portal here on the earth? Tesla too was obsessed with time travel. He worked on a time machine and reportedly succeeded saying, I could see the past, present and future all at the same time. In 1895, he almost killed himself while messing about with magnetic forces. It is thought he artificially created a magnetic field which he entered and could see history unfolding in every order, past, present and future. He discovered that space time could be altered and allow us to enter a different realm of reality. The idea that humans are able to travel in time has captured the imagination of millions around the globe. If we look back at history, we find numerous texts that can be interpreted as evidence of time travel. Considering the scientific advancements from the last century alone, might it be possible for future humans to have discovered the ability to travel in time? Are they, in fact, the so-called visitors that have been recorded throughout the centuries? Or are they otherworldly aliens who have mastered travel through both time and space? Perhaps the answers can be found not in the present, but in the ancient scriptures and texts that document so-called mythology. Of course, there are a number of modern experiments involving time travel, but have we yet actually discovered the sacred hidden ancient force? Who knows? In the words of the great Nikola Tesla, it is paradoxical yet true to say that the more we know, the more ignorant we become in the absolute sense, for it is only through enlightenment that we become conscious of our limitations. Precisely, one of the most gratifying results of intellectual evolution is the continuous opening up of new and greater prospects. What do you guys think of time travel? Comments below? Thanks for watching.


and stuff like that, and design that, and still look and write, write, write, write, write, write and stuff like that, and stuff like that, and stuff like that, and stuff like that, and write. Okay, now also, I also, can you please let me know what advice you have for someone who's starting on a creative project? Any type of advice you can give, no matter what area of the creative industry that they're starting on, any kind of some sort of advice you can give to them? Okay, I'll let them know that if it's a matter of passion, it's a matter of what you want to know, those constructive criticism that you get, but you have to know if it's constructive or not, or taking them to the investment quality, and then to a craft, and to know that they're starting on YouTube. Thank you. Mic check one two. That's looking really good. Mic check 1-2. Mic check 1-2. Yeah, it's looking good now. The sound is coming through. Okay. Okay, no problem. The man is simply incompetent.


Good morning everyone, on this last day of January the 31st Tuesday we're looking at the Dow down 6 at $33,710. One of the things we were looking at, at least I was looking at, was within the context of the Dow chart, it's just kind of stuck in a trading range, it's kind of a little bit overbought and I can see it pulling back a little bit here, if you look at the S&P which is, it was up quite nicely, now it is down, it's off the high, it's up 7 at $4,024, it went right to the resistance on the left side, that $4,100 area, it's pulling back a little bit here, the 200-period moving average of $39.96 is key support, we're looking at the QQQ, it's almost the same thing in each of the charts, the potential peak F in the S&P, potential peak F in the QQQ, it's up $0.34 at $2.9165, the weekly chart is starting to improve a lot, the IWM, the Russell 2000, of course this is buying day today, usually at the end of the month you get some buying pressure, we saw that from early in the morning, we're looking at the IWM up $1.22, holding quite nicely at $188.14, now this is going to be the issue here, gold was down very sharply, now it's up at $19.42, as I read it, the 9-period moving average is still way over the 14, the stochastic is now under 80% the Mac these week, but that 9 over the 14 says it'll take some time if it's going to have a digestive phase here, which I think is about to happen because the dollar is for the first time actually attempting a little bit of a rally, and we've got the dollar now down 9 ticks at 102.19, but today it went to 102.61, this does start a gray leg A in the daily chart, we'll see if we can hold, we're looking at the bonds TLT, TLT right now is trading at up 31 at 106.63, just stuck in a range, as I said, I think that yields are stuck in a range, and if you're looking at crude oil, look at this, crude oil is trading up 40 cents at 78.31, but in the lower range, so a lot of us says that you've got kind of a mixed market right now, it's very selective, some areas are doing well, some areas are just kind of filtering out, and if you look at something like an axon, which has been spectacular, it came out with earnings, and it is down 42 cents at 115.14, up in the higher range, but kind of digesting gains. I'll be back in a moment for the tidegate technicians out, check out my opening call date and use that, see you in a few moments. Great programming.


Time here for more systems and when I talk about link aggregation with PF sense, it's actually relatively easy to set up I'm going to walk through a couple scenarios and we're going to use a switch that supports LACP if you don't have a switch that supports LACP there are other modes of operation to still give you a little bit more BAM with essentially by tying the ports together or redundancy depending on what you're looking for But it is obviously going to work the best if you have a switch that does support LACP check the documentation for the switch you have to see if that's supported and Let's get started if you can click the like button and first feel like to learn more about me or my company head over to Lawrence systems calm if you like to hire short project There's a hires button right at the top if you'd like to help keep this channel Sponsor-free and thank you to everyone who already has there is a join button here for YouTube and a patreon page Your support is greatly appreciated if you're looking for deals or discounts on products and services We offer on this channel check out the affiliate links down below They're in the description of all of our videos including a link to our shirt store We have a wide variety of shirts that we sell and new designs come out Well randomly so check back frequently and finally our forums forums dot Lawrence systems comm is where you can have a More in-depth discussion about this video and other tech topics you've seen on this channel now back to our content And we'll start here with the manual What is link aggregation and link aggregation is where you're going to essentially tie some ports together to act as one? logical interface inside of pfSense this can be for redundancy this can be for Aggregating bandwidth together, but as a warning they do have this right down here using a lag does not necessarily guarantee full Thoroughput equal to the sum of all interfaces in particular a single flow will not exceed the throughput of a lag member Interface so in this video. We're going to tie two ports together, but that does not Mean the two one gig ports we tie together are going to automatically give us two gigs of bandwidth there is factors involved what that does mean is a Connection from my computer that may loop through this and go to another system and my computer is connected at one gig We're going to do the demo in a video for that. That's no problem. I can get the one gig What are what's the other one doing that? Well, we can have another session that also uses one gig So cumulatively individual flows can use the bandwidth of the ports But if we have a 10 gig connection and we're trying to squeeze it over down to the 2 gig Well, no that's still a single flow So even though we let's stay because we have a 10 gig switch here We started at 10 gig we go across the two it can not automatically Depending on the type of traffic if the each flow of the traffic can't exceed the single link This is where the confusion comes in a lot with how lag works So it's not an automatic you're just going to get the full power because it's assuming that it's one logical interface But it will put the data across there now main reason for doing this of course is you have Multiple flows that are going across and you want them spread across the other common reason for doing this Doesn't make sense when you're doing it with one switch But doing a lag interface between multiple switches for redundancy where you have PF sense Connected with multiple redundancies and you have the other devices behind it other servers Perhaps connected to multiple switches with lag redundancy that prevents a switch failure I've had some people say well shouldn't I use it because I have the extra ports and I need it because what if a cable fails? cable failures not unheard of but are uncommon switch failures way more common than a Failure of cable so if you want to do this in your home lab And you're saying I just wanted to do it because I have the ports and I don't like seeing them empty Awesome, you're not really gaining too much redundancy because the likelihood of a little cable failing less likely But hey it is there, but I'm gonna walk you through how to create the interface and how to set this up So let's go back over here to PF sense and We have a SG 51 hundred with a pretty basic load here in a land Now the first question I've had a few people ask me is can I just convert my land to be lag? Not exactly. So we're gonna go over your interface assignments Lagging when we try to add one here I have IX zero all the way through IX three available, but if we look at the interface assignments We see that lands assigned to IGB one and I can't include it in there This is actually by design. You can't add anything to a lag that already is assigned So you can't just flip a switch and convert your land over to lag yet to actually create a new interface Now I could just delete this right here because I'm actually logged in externally from this I'm logged in through the WAN side. So I can delete the land and just rebuild it. That's absolutely a possibility We're gonna go ahead and just create another interface All together and just walk you through the process For the first thing we need to do is pick out what ports we want to use We're gonna use the last two ports now the nice thing with you get an SG 51 hundred You're gonna have these labeled you have to figure out what parts they are if you built this yourself But the SG 51 hundred has all the port labels down below each individual port makes it really easy to figure out So we're going to use the ports right here on the end the two on the end which are labeled Ix three and Ix two So we're just going to go ahead and choose those like we have here And then we have to choose the lag protocol type now the lag protocol types are any explain They have a nice explainer over here And they're also explained in a manual where you can do failover load balance around Robin Warning if you do round Robin specifically it will try to just keep Sending the data back and forth on there and you actually seem to get a little bit less spam with when I was doing some testing with it Because it's going I'm gonna be helpful and just keep sending these packets some over here and some over there This round robinning actually seem to cut some of the performance. I got what I was doing this load balance might be a little bit more Intuitive for that and failover courses just failover now the other options down here failover load balance from Robin Don't require any special configuration of the switch because you're telling pf sense to handle it at the interface and look for the Outer interfaces, but this can create confusion. So if you set up a Failover and you have two switches and then the switches talk to each other if the link to where the switches talk to each other It becomes broken, but the link stays up between pf sense and the switches Now you have a problem where it goes I don't think I seen a fail because the switch didn't turn off, but it'll be confused as to how to communicate So the best way to do this is going to be LACP for the aggregation of bandwidth not in a failover situation LACP is going to be specifically to aggregate the bandwidth and that does require switch support So that's the one we're going to choose But like I said in the failover situation, you know you can do that for redundant for the switches and That works really well for that redundancy and maybe if someone asks I'll do a video on that But it's really just putting two switches together having them talk to each other and putting one link in each side of the failover I mean build on a bigger lab scenario for a failover demo with storage servers Which is actually an even more common scenario for this, but I have set these up in data centers where They have one leg of each of these going to each switch that way if they have a switch failure in a data center Their pf sense can talk and yes, this does work with the whole HA setup. You can bond together Multiple ones across HA across as it gets very complex very quickly But yes, it is capable of doing it and I'll leave a link to this This is also part of the netgate docs. They walk you through an entire layer to redundancy setup So like I said, you can get pretty advanced with this and it works really well But I'll at least cover the basics on how to get this interface set up and configured. We'll go here We're going to choose those two interfaces IX2, IX3, LACP and Laggy interface Pretty simple Then we're going to go over here to interface assignments because we now group them together now We have to assign the interface. So let's go here and we'll call it the laggy interface Then we click on it here just like any other interface because now they're bonded together And we'll call this Laggy LAN So it'll be our new LAN when we're done. We're going to go static Let's give it a static IP address of one two one six eight dot ninety nine dot whoops 99.1 and from here is pretty much the same standard interface set up So it's going to be LAN static 99.1. It's going to be a slash 24 save apply Firewall rules There's our laggy LAN and we're not going to dive deep into rules I have plenty of videos on that we're just going to do any any open it all up Let it fly let all the data pass through so no restrictions on this Then we're going to go to DHCP server on our laggy LAN here And we'll go from 50 To 250 plenty of range plenty of addresses on here. We've enabled it. We've got rules Save But now here's the important aspect that has to be done We have to go in and configure The switch to work right now We've got these ports doing nothing and if they're doing nothing, that's fine except they're not set up for lag So if you plug in LACP configured ports to these it's going to confuse the switch It's going to say I'm not speaking the same language and it will break So we're going to go in here and we're going to convert these over so currently this is plugged into LAN This is the port for on this right here. So we're actually going to move it over But before we do so I got to push the programming changes to this unified switch I see that because unified switches don't have an interface They use the unified software for the control plane So we're going to push the configuration But if you have a switch where you have a web interface on it It's kind of the same answer before you break it and have access to it You want to make sure you push these changes to it. We're going to go over here and configure port one And we're going to say Laggy PF sense so we're plugging in here And then we're going to go for the profile overrides And we're going to choose Aggregate what are we going to aggregate to ports one and two that means port one and two are going to get assigned the LACP protocol now if we were using all four of the ports We could just change that to a four or even a three if there's three of the ports and so on and it's going to grab All the ones next to it We only need ports one and two because we set up only a two-port setup gonna hit apply And we watch it provision right here and so this time provisioning then we can plug it in and get this set up on the other side So it provisioned the settings have been changed and now if we look at this one We look at profile for port two. It's aggregating from there now comes a pretty simple part we're going to move this over to the other side, so we're going to grab a little cable here and Plug them in like this. So we did port one We did port two And we have them down here Actually, we'll slide the switch down. There we go. So now those two end ports are plugged into port one and two now The order itself doesn't matter This is LACP. This is going to communicate LACP to this This is going to have to take a second to get a new IP address because well we changed IPs We're not using the LAN anymore matter of fact while we're waiting for that to think and get connected Well, I'm going to speed up the process by power cycling it So I pull the power out power it back on while that's doing that. We're going to go back over here to PF sense And remember I'm connected to the LAN so none of this really matters that this part happened at all And you can see that currently LAN is down and if we wanted to we can just go over here to interfaces LAN I could just disable this interface. I don't even need it anymore We're not going to use it and the other one can become everything I do for LAN Jump ahead a couple of minutes while this booted because I Realized and for those closely looking at the detail familiar with this switch that first ports the console port This is port one. I was actually troubleshooting something that I plugged in this way So yes, I did plug it in accidentally to the console port didn't hurt anything But it certainly didn't Allow the two interfaces to work So now that we haven't plugged in their proper interface and the switch is booted up And we have our lag interface configured we can look right here and we see Lag interface ports one and two and this is just the aggregate port interface. So now we got the two redundant interfaces Let's go back over here. We look at the status and we have it set right here So we have laggy LAN auto select and we see that it's up and our LAN is down a couple side nodes over here We're going to go status system logs Now one thing I want to show is We're going to drop an interface. We're just going to take this We're going to accidentally lose an interface plug unplug one and kind of show what pfSense and how that handles it So we get back over here after we unplug it refresh the page We do get a link status down So with the link status down as I mentioned though and laggy LAN here It still shows up because still one of them is up just not both of them are up So technically we do have a connection So plug that back in then go back over here to status system logs System state change back to up So pretty straightforward there next we're going to take this network cable here and plug my laptop in So my laptop is going to get plugged in with the extra ports here not into the console port won't make that mistake again So now my laptop should get an IP address hand it out by the pfSense through the switch through the LACP lag interface or lag LACP so technically LACP is a sub protocol of lag for those that are probably going to call me out on that little detail Let's uh, see if I get an IP address on this move this over and there's the IP address I got 99.101 and let's go ahead and ping the pfSense which is at that 99.1 pretty straightforward it pings so while it's pinging and so you see what I'm doing right here I'm going to drop one of the connections and watch the pings And it's going to pause for a second while it figures out. Oh, you need to go across the other path This is how the redundancy works. It's pretty seamless except this was a packet flow coming from one system So because LACP would be figuring out the flows from different systems and putting them across the connections Which well cable that goes across is going to be a little bit Not the word random isn't there, uh, but now that this one's coming up and down It's going to go over here once it decides which cable is going over it goes over there unless there's a change in topology So now that we know it's going probably across the black cable We'll go ahead and do this unplug it. Oh went back across this one But now that it's going across the other cable now we're going to plug this back in so listen for the click It doesn't pause to start the flow back on the other side This is how LACP works with the lag and the protocols together Once it decides which cable it's going over that flow will continue to go over that cable And it's dynamically figuring it out. That's the advantage of the way this protocol works Now a couple are side notes inside a pf sense of how this works in terms of how about v-lands or everything else Actually no change there So even though the interfaces are bonded together because they're bonded together as They're the physical layer is bonded together to work as a single interface As as we're calling it laggy land we go to interfaces assignments And we do something like a v-land and we add and we say we want a v-land tag I don't know 88 just so we have something 888 sure why not you choose the parent interface and the parent interface is going to be lag zero So all the other rules apply. So by doing that there's the parent interface and we go back to the assignments We can then assign v-land 888 to here and then there's no change inside the unify software when you assign a V-land it still just works the same. It's not going to be any difference Just because you're lagging these together. So you can still and we can edit these ports for example And I have a v-land test 1 2 3 in here I'd have to define it in here if I wanted to use v-land 88 like I did in there But you get the idea you can even assign to lag interfaces the v-land now It's going to be varied how this works with different model switches But it's not a big deal in terms of how it works including when you're building out the storage network Maybe you want a dedicated v-land just for all your storage devices. You can lag those interfaces together You know obviously lacp and that dependency So is required in the switches if you want to use full lacp But it's that easy to set up in pfSense. It's pretty straightforward It's works just as another interface. So any other videos I've done where I'm talking about assigning something to interface Once you build the lag interface the way you go. It just works now one last thing What if you wanted to add one more? Well, you can do that So we're going to go here and first well as I said yet They'll always make sure we have the switch on there. So we have one two three now So we're going to apply this And we're going to let this configuration push while we're doing that. Where's that third interface going to come from? Well, go over here to lag You can edit these because we still haven't assigned anything to ix one So it's still just an empty port and hit save So now it's going to apply this here. We're provisioning the switch So we'll give the switch a second to catch up. But while we're doing that we go over here Snap and they're crisscrossing the cables here, but you get the idea Um, now I've got all three of these ports and all three assigned to this same rules apply and Now it's just lacp is going to talk to you all three ports. Let's see if the switch provisioned Yep, it pushed the provision on there. So now it says Port two port three And that easy now you didn't have to do this now this would disrupt users But you didn't have to do anything Else in pfSense to add more to this aggregation group. We've just added one more We could just as easily drop one from it now when you do this there is a disruption in network So if you're routing a bunch of traffic over it and you change these assignments When it does configure the switches there is a disruption to rebuild them into the link but hey, that's not that big of a deal the disruption is pretty minor And happens pretty much fast. We do this essentially in real time So if there's someone on a void call that are going to be angry at you because it may drop the call But for the most part it's a pause in the internet and everything keeps working So i'll leave links to the pages and the documentation from netgate on this to dive deeper into this and Leave comments below or head over to forums and you know talk about maybe Suggestions you have for having a lab about a larger setup or install But i am going to do another video on this topic related to doing this with storage servers. All right, thanks And thank you for making it to the end of the video If you like this video, please give it a thumbs up If you'd like to see more content from the channel hit the subscribe button and hit the bell icon If you like youtube to notify you when new videos come out If you'd like to hire us head over to laurancesystems.com fill out our contact page And let us know what we can help you with and what projects you'd like us to work together on If you want to carry on the discussion head over to forums.laurancesystems.com Where we can carry on the discussion about this video other videos or other tech topics in general Even suggestions for new videos. They're accepted right there on our forums, which are free Also, if you like to help the channel out in other ways head over to our affiliate page We have a lot of great tech offers for you. And once again, thanks for watching and see you next time