Welcome back, we were discussing the loss of large numbers in particular for IID random variables. We said that the weak law of large numbers says that the sample average converges in probability to expectation of x. And similarly, the strong law of large numbers says that the same sample average converges to expectation of x almost surely right. So, these two results we will prove today. Strong law of large numbers we will not prove in full generality because it is a fairly long proof. We will prove it for with slightly more additional assumptions. So, first we will do the weak law of large numbers. So, if you remember you have. So, x i are IID random variables with expectation of x finite. Then we have to show. So, we have to show that this average converges to expectation of x in probability. So, there is actually let me do two proofs. So, one of them is a very simple proof which assumes finite variance. So, the theorem itself does not assume anything other than finite mean. But, if you assume in addition that the variance is finite the proof is very easy. Again the theorem does not require finite variance, but the proof is easy if you assume finite variance. So, partial proof. So, if you assume sigma x square this finite in this case it. So, turns out that you can prove mean square convergence very easily. So, in particular. So, this is S n over n. So, we have expectation of S n over n is equal to expectation of x because expectation of S n is nothing, but n times the expectation of x. So, this you will agree. So, what I am claiming is I will be able to prove the mean square convergence of S n over n to expectation of x. And since mean square convergence implies convergence in probability I will be done. So, you consider expectation of S n over n minus expectation of x square. So, I want to claim. So, if I prove this limit goes to 0 as n tends to infinity I would have proved mean square convergence. Now, this is S n over n minus expectation of S n over n. So, this is nothing, but the variance of S n over n this whole term is the variance of S n over n because this is the expectation of S n over n. So, this is equal to variance of S n over n which can be written as variance of S n over what n square. Now, what is variance of S n? See S n is the sum of the first n x i s. Now, these are i i d random variables. Since, they are independent you can add their variances to get the variance of S n. So, the variance of S n will be equal to n times the variance of x i and which is assumed to be finite. So, this is equal to n times sigma x square over n square. So, this n cancels. So, you get sigma x square over n. So, this mean square go as n becomes large goes down to 0 as 1 over n. So, this goes to 0 which means that S n over n converges to expectation of x in the mean square sense. And then mean square convergence implies convergence in probability because of chebyshev's inequality then you will have convergence in probability. So, it is really a very simple proof there are only 3 4 steps to it. If you assume finite variance it is very simple. But, that is just a partial proof because this proof only works when the variance of x i is finite. You may have a situation where expectation of x i is finite expectation of x is finite. But, the variance is infinite that is possible as we saw. Can you think of an example?  The law of large numbers does not demand that the variance be finite. So, this proof is not a complete proof. So, you want to do a full proof. Full proof is also easy, but you have to invoke characteristic functions. So, what we will use is that we will prove that the characteristic function of S n over n the sequence of random variables S n over n converges to the characteristic function of this constant random variable. And then I would have proven it because if I know that the sequence of characteristic function converges to a legitimate characteristic function. Then I have convergence in distribution. Now, convergence in distribution is same as convergence in probability if the limit is a constant. So, I would have proved my result that is what I will do now. So, consider the characteristic function of S n over n. So, I am looking at expectation of e power i t S n over n. This is what I am looking at. So, this I can write as the expectation of e power i t over n times S n. Now, the reason I did that I took the n to the t is because now this looks like the characteristic function of S n not evaluated at t, but evaluated at t over n. But what is the characteristic function of S n? S n is the sum of these i i d random variables. So, I can multiply the characteristic functions. So, it will be the nth power of the c x of t. So, that is fairly simple. So, this will work out to c x of what does it work out to c x of it has to be evaluated at t over n whole raise to n correct. Next since expectation of since expectation of x is finite c x of t admits the following expansion. So, you can write c x of t as 1 plus i expectation of x times t plus little o t, t squared I think. Little o t or t squared is actually I think little o t as a matter of fact. It is order t squared terms little o t. This is because if the k th moment is finite you can expand till the k th moment and write a little o term. This is the property the moment generating property of characteristic functions. Now, so the excellent. So, you can write this guy as thus expectation of e power i t S n over n. So, the characteristic function of S n over n is that guy. So, that looks like all this right. So, 1 plus i expectation of x t over n right I am writing t over n instead of t plus little o little o of t over n whole raise to n. Now, as n tends to infinity what happens to this. So, this little o term looks like it goes to 0 faster than it goes to 0 like t squared or something t squared over n squared the smaller terms. So, as n becomes large this will become very insignificant correct. So, for all practical purposes this will look like 1 plus i expectation of x t over n whole raise to n right. So, in the limit as n tends to infinity what happens this will become e power i. So, this is like 1 plus z over n whole to n right which is e power which goes to e power z as n becomes large correct. So, this will converge to e power i t expectation of x for all t. So, this means the characteristic function of the sample average as n becomes large if the characteristic function converges to this is the characteristic function of the constant random variable. If you call this constant c right the constant random variable c has characteristic function e power i t c. So, this is the characteristic function of the constant random variable expectation of x right. Now, view expectation of x as a number not as a number, but a constant random variable right. So, this will be the characteristic function of the constant random variable expectation of x which means. So, this implies s n over n converges to expectation of x in distribution that is because we proved a theorem saying convergence of characteristic function to a valid characteristic function implies the convergence of distribution. But now the limit is a constant right convergence in distribution to a constant is same as convergence in probability right. So, this implies s n over n converges in probability to expectation of x. So, this looks like. So, this terms are terms that are going to 0 faster than t over n. So, there is a t over n term n is becoming big right and these terms are becoming very small and. So, for all. So, you can prove this you can prove that you know that 1 plus z over n to the n goes to e power z right that you know for every complex z. Now, you have a little bit more, but that little bit more is very small. So, that does not affect this convergence right. So, this as n tends to infinity this characteristic function converges to e power i t x. Any questions? So, here we have not assume finite variance characteristic function proof is a fully general proof correct. Are there any questions before we move to strong law? So, expectation of x is always a constant, but I am saying that the constant random variable taking value let us say c has characteristic function e power i t c right. So, I am saying this is the characteristic function of the constant expectation of x that is all right. So, let us move on to the strong law of large numbers again x i's are i i d expectation of absolute x is less than infinity you want to prove that s n over n converges to expectation of x almost surely right. So, the proof of the general proof of the strong law is quite long. So, what I will do? So, just like here I did 2 proofs right. One of them was a partial proof assuming something more and then here is a completely general proof. So, for the strong law what I will do is I will give you 2 partial proofs and I will mention how it is extended. So, the first partial proof assumes that the fourth moment of x i's are finite. So, you have you assume a little more, but not even finite variance, but finite fourth moments. So, it so happens that if you assume finite fourth moments of x i's are finite then you have a very simple proof of strong law the very elegant proof it comes out very nicely. But of course, fourth moment it is a fairly strong assumption as assuming that fourth moment is finite. So, I will give you another partial proof that only assumes finite variance it is a little bit longer the second partial proof we assume only finite variance. And then of course, if you do not even assume finite variance you have to it is a fairly long proof actually the proof is there and grim it runs to about 3 pages or. So, it is long, but not horribly wrong it is not 40 pages long right as some proofs can be. So, I will do 2 partial proofs partial proof assume expectation of x power 4 x i power 4 is some eta x some finite number also without loss of generality assume expectation of x is 0 actually the reason I say there is no loss of generality is we can get it back. So, if x i's have some non 0. So, they have finite mean right if they have finite fourth moment they have finite mean you subtract the means if they have non 0 mean right you define x n tilde equal to x n minus expectation of x and then prove the result for x n tilde and then you have to go back to proving it for x. So, this without loss of generality can be justified there is no loss of generality in assuming that all these random variables are 0 mean. So, what you have? So, you have assume finite fourth moment. So, you have so you will do this I think. So, you will so let us look at the probability of the fourth power x i epsilon and. So, this is less than expectation of correct Markov now I am going to complete well let me write it this way as I know absolute s n to the fourth over n to the fourth epsilon to the fourth. Now, I am going to compute this guy absolute s n to the fourth is same as s n to the fourth right this is fine. So, I just took the absolute value out because the fourth power I mean it does not make a difference right because you are taking the fourth power anyway. So, if you look at expectation of s n to the four that will look like expectation of x 1 dot x n to the fourth. So, now I am just going to expand this. So, you will get n. So, you will get the fourth powers of all x i's and there will be n such terms correct. So, this will be equal to n times eta x I will have you will have n times eta x as the first x. So, you will have x 1 to the fourth plus x 2 to the fourth plus so on right there will be n such terms correct plus what else will you have you will have terms that looks like x 1 x 2 cubed and so on correct all possible pairs of x i x j cubed correct where i n j run over all indices correct. Now, what is the expectation of a term like that what is the expectation of x i x j cubed say they are independent. So, you can write it as expectation of x i times expectation of x j cubed, but expectation of x i is 0. So, all these odd terms will go to 0 all these x i x j cubed terms will go to 0 and what else remains you will have terms that look like x 1 squared x 2 squared right x i squared x j squared you will have right how many of those do you have you will have I believe you will have. So, you can do n choose 2 of these right and then you will have to do 4 choose 2 right. So, you will have something like 6 times n choose 2. So, many terms of x 1 squared times x 2 squared expectation of x 1 squared x 2 squared correct. So, just x you are you have 4 of these write it out. So, you will have expectation of x 1 squared times expectation of x 2 squared which is nothing, but sigma x to the 4th right and all other terms will be 0 this verify this I am not I am not 100 percent sure about this I think this is correct, but you will essentially you will get something that looks like n squared times sigma x to the 4th. This is just algebra this is just expand the whole thing out and you making use of the fact that x i is at 0 mean. So, the terms that look like x 2 x 3 cubed will go to 0 in expectation correct and this comes because you are taking you are taking. So, you are looking at terms like x j x j squared x i squared x j squared and i n j you can pick in n choose 2 ways is not it and there are 4 places where you can pick the i's and j's from 2 2 out of 4 right which is why you get 4 choose 2 which is 6. And then you have expectation of x 1 squared times expectation of x 2 squared which is sigma x squared times sigma x squared which is sigma x to the 4th. So, now you have so this is good. So, expectation of so if I go back here. So, let me put that back here all right. So, this I will get. So, I am going this here. So, this will be equal to what I have eta x over n cubed epsilon right plus 6 times n choose 2 is 3 n n minus 1 right. So, let me just upper bound this as actually let me just write 3 n squared over n to the 4 epsilon. See 6 times n choose 2 I have upper bounded by 3 n square like 6 times n choose 2 is nothing but 6 times n n minus 1 over 2 which is 3 times n n minus 1 I am upper voting that by 3 n squared. So, great. So, what do I have? So, I have that probability of S n over n to the 4th exceeding epsilon is less than all that right. So, I will actually I will get it of this n squared will cancel with the n to the 4th to give you n squared epsilon correct. So, what do you have? So, this implies that sum over n equals 1 to infinity probability of S n over n to the 4th. So, if I sum from n to n equal 1 to infinity what will I get? That will be less than it will be less than infinity for all epsilon because this is less than that. And if I sum this from n equal to 1 to infinity I have a 1 over n cubed term. And I have a 1 over n squared term they both finite as long as I do not have 1 over n I am fine right. So, this will be less than infinity. So, what does this imply? So, we have seen this right by from Borel Cantelli lemma we saw if probability of X n minus X greater than epsilon the summation is finite then X n goes to X almost surely. This means that S n over n to the 4th goes to 0 almost surely from which you can show that S n over n goes to 0 almost surely. So, this implies S n over n to the 4th goes to 0 almost surely from which you can argue that S n over n goes to 0 almost surely. This is a very short proof of the strong law you prove this for 0 mean. Now, you can put back the beam you can take this X i this X i you can take as X i X i tilde which is X i minus expectation of X right. And then you can prove for non 0 mean also any questions on this. So, from here how do you conclude that S n over n goes to 0 almost surely. So, the set of all epsilon's where see set of all omega's where S n over n to the 4th goes to 0 for those omega's S n over n will have to go to 0 right saying that the 4th power of a sequence is going to 0 right. This means the sequence has to go to 0 actually you know what. So, I am going to keep this. So, I was about to erase this, but I am going to use this. So, I will erase this. So, I am going to if there are no questions on this I will give you a another partial proof of the strong law of large numbers. This time I will only assume finite variance. So, this assume something very strong right you assume 4th moments of finite which is a very strong assumption. Now, I will do for finite variance. So, once you prove it for finite variance then you have to in order to generalize fully you have to go through a truncation argument. You have to truncate these random variables at some big value b. And so the truncated random variable will have finite variance right. And then you have to show that as b is very large the truncated random variables and the original random variables are close. And then you will get your strong law. So, partial proof 2 assume now that sigma x squared is finite. And let expectation of x is equal to mu. So, begin we assume x i's are i i d non negative random variables. So, we will prove strong law for finite variance non negative random variables. So, in that case so we know that from. So, you call this equation star from star we have. So, I have a bound on the mean squared. So, I am going to look for. So, I am going to look at this guy S n over n minus mu mu is my mean by the way I am going to look for this probability. So, this probability is less than by Markov this is less than sigma x squared over n epsilon agreed correct why is this. So, this is because this will be less than expectation of that squared over epsilon squared. So, just a minute. So, I think there should be an epsilon squared here or if I have. So, I should probably have epsilon squared here. So, they be a square here. So, all I am saying is I am skipping a step here. So, this greater than epsilon is same as yeah. So, this squared exceeding that squared right which means by Markov this is less than expectation of this squared over n times. So, the over sorry epsilon squared. So, there should be a squared correct, but I know that expectation of that object squared is sigma x squared over n. So, agree with me on this. So, all these squares can go away yeah. So, this you will agree right this is basically just actually come to think of it this is just tabby shape inequality right. This is x minus mu greater than epsilon is less than or equal to the variance over epsilon squared correct and variance is sigma x squared over n. So, yeah correct. So, this is 100 percent correct. So, now, this from this if you take limit n tending to infinity you will get 0, but that only help you prove convergence in probability right does not give you convergence almost surely correct. So, you have to somehow jump from convergence in probability to convergence almost surely. So, you can jumping from convergence almost surely to convergence in probability is trivial right it always is true, but you know that there is a partial converse going from convergence in probability to convergence almost surely. Recall that if you submit you will get something that is. So, that guy is not going to be finite that is not going to help you here right find a subsequence you find a subsequence. So, what subsequence will you find now. So, there always see when you have convergence in probability there is always a subsequence a deterministic subsequence that goes to the same limit almost surely correct. Remember the theorem and that subsequence is deterministic it does not depend on omega right. So, I think I mentioned see you have this occasional epsilon excursions in this convergence in probability, but by choosing the subsequence you are able to avoid these excursions right. So, the nice thing is you can choose these subsequence irrespective of the realization see I mean if your subsequence can depend on the realization it is no big deal right I can avoid precisely those excursions right that is not surprising at all. But, I can choose a subsequence which avoids deterministic before hand before even omega realises. So, that I do not have these extra long excursions and therefore, I have convergence almost surely. So, if you consider here. So, what do you think should be the sequence there should be a subsequence of this n. If you go in like k squared if n k let n k equal to k squared. So, the reason I am doing k squared is I want this to go to 0 faster now actually I do not need k square I can even take k to the 1 plus delta, but this is fine. So, I am not looking at s 2 over 2 s 3 over 3 s 4 over 4 and so on I am looking at for the perfect square right k equal to n equal to some perfect square I am looking at that sequence. Then what happens is probability of s n k over n k minus mu you just look at that will be less than omega x squared over n k epsilon square and n k is equal to k square. So, that will be k squared epsilon square. So, if I sum this over k now. So, this is a subsequence n k right index by k. Now, if I sum this over k I get something that is something finite right which means the sequence s n k index by k s n k over n k index by k goes to 0 goes to mu almost surely correct. So, if you have thus sum over k equal to 1 to infinity probability of s n k over n k minus mu greater than epsilon is finite. Because, if you sum this over k equal to 1 to infinity you get something finite right for all epsilon this means s n k over n k goes to mu almost surely as k goes to infinity. So, this is not all that surprising because if you know that s n over n goes to mu in probability. So, they must be sums subsequence s n k over n k which goes to 0 goes to mu almost surely by the theorem right. The good thing is we have identified what that n k is its k squared is enough right. So, that is good now can I actually now that is not enough right I have to prove that s n over n goes to mu almost surely. Now, that is where this assumption comes in. So, this non negative assumption is going to help us now. So, what happens if so next if you consider. So, you are looking at s n over n if k n is a perfect square this helps you right whenever n is a perfect square those terms go to 0 almost surely. But, what if n is not a perfect square right. So, in that case you have to prove. So, you have to look at. So, let say n is some 13 or something look at the number which is the perfect square which is smaller and the next number which is bigger next perfect square which is bigger. So, you can write this is not it s n will lie between. So, since x i is a non negative s n can be bounded between s. So, let me write it like this s k plus 1 squared and s k squared where s squared is less than or equal to n is less than or equal to k plus 1 squared. So, if n is not a perfect square you find the next smallest and the next biggest perfect squares. Well, maybe you should have that less than you can always do that and why is this true because your x i is a non negative. So, this s i can only increase. So, this you will agree with now ideally I want. So, I want some sandwiching argument to go through right. So, I am going to divide this by n which is what I want right. Now, what should I divide this by in order to preserve this inequality. So, let me just divide all of this by n that is definitely fine right. So, I should write that as s k plus 1 squared over n right. I am just dividing everything by n then I can write one more term. So, I can write this is less than or equal to s k squared over. So, I have to divide by something larger. So, I can do I cannot do k squared right then this inequality would not hold right. Then here I have to do a similar trick. So, if s k plus 1 squared over now what do I do instead of n I write I cannot write k plus 1 squared. So, I write k squared. So, you agree with that right this is just algebra. Now, I send now I send n to infinity if I send n to infinity k also goes to infinity. So, k goes to infinity what happens to this term. See I know that x k squared over k squared goes to mu almost surely which mean x k squared over k plus 1 squared also goes to mu almost surely you see why well because it is again just simple algebra right. So, send a k n to infinity. So, then you will have. So, as n tends to infinity k will also go to infinity. So, limit k tends to infinity s k squared over k plus 1 squared less than or equal to limit n tending to infinity s n over n less than or equal to limit k tending to infinity s k plus 1 squared over k squared. So, I have so I have a sandwiching argument coming up right. So, this as k tends to infinity. So, this guy can be written as s k squared over k squared times k squared over k plus 1 squared. So, limit k tending to infinity of that correct, but as limit k tends to infinity the almost sure limit of this is mu and as k tends to infinity that goes to 1 that deterministically goes to 1 right. So, the limit of this as k tends to infinity is almost surely equal to mu right. So, this is this limit is almost surely equal to mu correct and similarly this is also almost surely equal to mu. So, therefore this limit exist almost surely see right, because this guy is this limit is sandwiched between 2 objects which are almost surely converging to mu right. So, this limit exists almost surely and that limit is equal to mu almost surely right. So, that is the sandwich argument. So, as n over n goes to 0 goes to mu almost surely we have assumed finite variance and we also assumed non negative random variables right. So, to extend possibly negative random variables with finite variance right x i is equal to x i plus minus x i and proceed. So, the same trick right x is equal to x plus minus x minus and so you can get rid of the non negative assumption. So, for finite variance random variables we have more or less we have actually proved the strong law of large numbers. So, in order to remove this finite variance assumption as well you have to as I said you have to do a truncation argument you have to define x i delta equal to max of b comma x i right. So, you truncate these random variables x i when they take very large values greater than b some b you call it equal to b. Now, this truncated random variables will have finite variance. So, the law will go through right and then you have to make sure that this b goes to infinity in an appropriate at an appropriate rate. So, that is where the difficulty is that is it is not very conceptually very demanding it is just messy. Actually Grimit has a full proof of without any further assumption it has a proof and also Terry Tau's blog has a very nice exposition on the strong law of large numbers you know the famous mathematician Terry Tau his blog has a very good article blog on strong law of large numbers you can read. I will stop here.


So identifying aquatic plants can be quite difficult. A lot of people get nervous when they get across them. People haven't spent much time looking at plants and looking at different parts. So today I'm going to try to show you guys different components you can look at on plants and to help you ID them or to send them off to an extension specialist or a regional biologist so they can help you in assisting and figuring out what these plants are for you. So over here I have a range of different plants. They range from russus, sedges and even just broadleaf plants. So the first thing that we kind of look at is where is the plant growing? Is it growing emergent like against the shoreline or breaking through the water? Is it submerged where the roots are still in the soil or the water bank and growing under the water surface or is it truly floating to where the roots are hanging from the surface of the water and not penetrating the soil below? So once you have that you can kind of go on and look at the leaf structure and arrangement. A lot of these plants will have different kind of leaves whether they're growing at different nodes or just a straight up stalk and you can look at different arrangements such as alternate opposite and whirl. So opposites when they're growing at the same node on the same part world will be growing around the stem in a circle and then alternate will be switching back and forth on different sides. So here we have different things such as different russus which are typically round not to be confused with sedges which is typically done sedges have edges but both of these things are not truly true. Some sedges can be round and some russus could have edges. However the most helpful piece anyone can do to identify plants is looking at a seed head the flowers or the inflorescence. So an inflorescence is a cluster of flowers found typically on the stalk of a plant such as on this rush or even on this sedge. Also different other kind of leaf structures we have is kind of like the Sagittaria which is common aerial head it's known by a distinct two flaps coming down and then we also have some more grass like plants. If you notice on this there's different nodes which are the big suspended areas and a helpful place to identify these kinds of plants is to notice that the leaf is attached directly to a node or if it has a sheath coming off of it instead. So keep holding it to why we need to identify plants is when we treat them in ponds or small lakes and pound mints and such the different herbicides affect different ones more effectively so whether they're broad leaf or just submerged in the water we have to use a different herbicide to effectively kill it control it or manage them. Now if you're unsure of a plant and you need a storm for later on used to be sent on to a biologist you can attach to put them in a ziploc bag with a wet paper towel on it and try to get just the paper towel damp store as much of the plant as you can we're talking about as much as the roots the stem if you can get a flower influorescence that's very helpful and just store it in a damp bag make sure a damp paper towel in a bag and try not to seal the bag all the way just the majority of the way so that the plant can still breathe and live for a little while longer


Check it out, folks. I'm back at it again with another breakfast with AB. Now, check this out. Today, I'm gonna show you guys just how easy it is to make. And when I say easy, you can look down at these ingredients. I'm gonna show you how easy it is to make just a breakfast skillet.  I always use thick cut bacon, you know? Then look, you got bell peppers. Potatoes is gonna be the main thing. And then we gonna go ahead and get the food police, the political people and everybody else about putting these eggs in there. Because you know what? I'm gonna do mine over easy. Let's get it. Now, I'm gonna go ahead and just do my slices. I'll give you guys a little bit of a pro tip. If you put your bacon in, say, like a cold cast iron and then you bring the temp up, that'll keep it more straight. Notice I don't have nothing down. I'm just gonna put these down like this. Hey, I don't know about you guys, but you gotta get yourself one of these splash guards, right, the splatter guard. Protect your counters, easy cleanup because there won't be no mess. All right, so look. Now, I'm gonna go ahead and take my bacon out.    We don't wanna just like put it all back into our food, right? So we'll just put it like this. Then when we're done with this, we're gonna go ahead and start working on our sausage. Okay. Now we gotta talk about saving your bacon grease, right? Obviously I'm good here. Don't forget we're getting ready to go into the holidays. So I'm gonna need all of this to make my food just super delicious. And I'm starting my second one. All right, so like I said, holidays, folks. I'm just gonna go ahead and just start putting those in just like that. Now remember, I'm using cast iron.  So I don't know how many of you guys make these little link sausages like this, but these are very outstanding. And I went with the maple version so they like soaked in that maple. You can smell it. All right, so if you guys take a look, you know, we just brown them on all sides, right? You guys can roll them across like this. I see a couple that Mike can use just a little bit of browning, you know, like that. But for the most part, they really done. You don't wanna like overcook them. You don't want them to be dry, right? I like my sausage to just be nice and juicy, right? So we look at them like this and then to always make sure. But me, especially, you know, just like I'm teaching, right? We just gotta make sure. So if I stick this in here like that, get that back, 158, it dropped to 160. Let me raise in 165. That tells me, look, that's right. You guys gotta get yourself one of these thermometers, right? These meat thermometers. If you pay attention, look, make for a great gift. And look, you see right there where I say smoking and grilling with AB? Go ahead and get it. They make for great gifts, folks. Check it out, folks. Now that's fire. Look at that. So I just put it down here in the center. Go ahead and close it. Get it close to the center as possible down there. And just give it some elbow grease. Now you guys can cut your fries any kind of way you want to. It's gonna be a method to my madness. I'm just gonna set that off to the side. After you see me cut these, look. And if you pay attention, let me just put them like this. I did them like this so you guys would see. I have four potatoes. I cut this one in half. So this one and this one make one. And these are whole, right? So I'll just stick it over here like this. The reason I cut them like that and I kept the skin on, look, you're gonna like this. Now you guys can cut them however you want to. But if you take them, since we're gonna make, you know, some home fries, not really home fries, we just cube them, making them like a hash brown type. You know, set up, look at that. You see how they are? That's what you wanna get. Look at that right there. Everything nice and hot. It just got a little splash from my gloves, right? So I'm just gonna make sure I'm at a medium flame. You wanna have it nice and hot, then you wanna make sure you rinse it. So now, remember all that flavor we left on the inside of the pan? This is how it's gonna come out right. Right, now I'm just trying to maximize, all of it's not gonna go ahead and get in there like that. But this is gonna be enough. Now what you wanna do is keep it at a nice high heat, let it settle, leave it alone, and let it brown. I'll be seasoning, I'll be using my original, listen, this is my AP seasoning, right? My AP seasoning is a little bit different than everybody else's. Everybody do that salt, pepper, garlic thing. I just ask you guys to give it a try, come back, and let me know what you think, or just read some of the comments, right? So you'll see, I'm not trying to overpower it. Right, I just put a little bit on top of there. Now, listen, that's a low sodium product, right? So I know, I just give it like a generous, a couple of generous pinches of salt. Now I got both of these pepper meals right here. I just wanna show you. This white right here represent white pepper. If you're going for something with a little bit of a different flavor, I call this the ooey. This is more traditional, everybody having it. This would just be the fresh ground black pepper. I'm gonna do this right here, because listen, you can see it. And then I'm finna give it a stir, let it cook. You know, try to get some of these ones that's on the top, get them down on the bottom. You know what I mean? And then we finna add our onions. Now, after looking at this, knowing that they almost are about ready, now it's time to add our onions, right? You guys, look, I diced these a little small, a little bit bigger would have been nice. You know what I mean? Just remember, small dice is for flavor. Larger is for texture, right? So we'll just get this going and start working on that. All right, folks, look at that right there. That right there looks amazing, doesn't it? So look, now I'm gonna go ahead and just cut this down. You know what I mean? Just kinda like give it a chop. I still wanna be able to see it. If you ask me, I probably should have made more bacon and not to mention that everybody wants to like keep reaching in here. Like, ooh, let me try a slice. Somebody just had some that told me they don't even really eat pork. I don't understand that one, but anyway. Also, you guys, you can see that I'm using my knife, right? Look, smoking and grilling with AB. Listen, the holidays are coming.  Guys, gotta check me out. Go by my website, check a look down in the description box below. Listen, these are the tools that I use. I only recommend what I recommend, but this one right here is fire. Stainless steel, going your dishwasher, the whole shebang. Right, so now I'm gonna go ahead and just cut these down like this. I don't know about y'all, but they got a place that rhymes with penny. You know what I'm saying? I'll just leave it like that. You know what I mean? They got the skillets on lock. This one right here, I wanna tell you though, they ain't got my seasoning. And this right here is fire, folks. So I'm gonna go ahead and make myself a couple of little indentations right here. If you do the over easy or whatever type of egg you do, you're gonna need to have a lid. If you don't have a lid, get yourself some foil. Put the foil over the top so it can steam and cook, right? So now we'll just put this here. I'm gonna grab this. And what we're gonna do is, we still got that medium flame. I got a little heat coming up off the bottom of here. Now we just go ahead and break them, right?  I do. You guys can do it if you scramble them. You can season everything in the inside. Then when I come with my kosher salt, I just give it just a little bit like that. One pinch should do four eggs, right? We do that and then we just add the top and now we cook. I look at my eggs and let that judge for me too.  Why? Because I don't wanna like super steam my potatoes. I don't want them to be mushy, right? So now I'm gonna come with just a little bit of my cheese. I'm gonna put the top back on there but we let a lot of the steam out already. Okay folks, just from the residual heat, right? Let me just go ahead and take it off. So you guys can look at it right there. As you can see, it's a little bit on the melted side. Ask what I like. Now I'm putting a little bit on here because you know what, I love cheese. We gotta have some green, you know what I mean? But look at this right here folks. And you tell me what do you think? Okay, so if you guys come on in and take a look at this now, I just leveled it up with a little bit of avocado. You know, I'm from the West Coast, folks. You guys see me when as LA had. Yeah, that's right. I'm from Los Angeles, you know what I mean? And then coming from California anyway, everything just about got avocados on it anyway. So with that being said, got that. Got a clean cut and dice. Now I gotta take some pictures of this. I gotta take some more pictures of it, right?   You know what I mean? Just, oh man, I really wanna go in there. Oh, gotta get some of that too. I'll just put it on there like that. Oh, oh, and we gotta get some veggies. You know what I mean? That's what I meant when I want you to see the integrity. Like the veggies, the potatoes, everything is just cooked just right. And then with a little bit of steam when you put the top on. Listen, I feel like I'm over talking it. I don't want to do that, folks. So guess what? Hey, and then for the food police out there, be telling me I'll be eating over the food. Let me take a step over this way. You good? Cheers. Now check it out, folks. I didn't put a whole lot, you know, when I got me a taste test, you know what I mean? To even really be wiping my mouth. You know why? Cause I gotta finish this up. But when I do, I'm finna devour this. Now, let's go ahead and start that debate. Talk to me about these eggs, folks. What would y'all do down at the bottom? You know, down in the comment section below. I know y'all are gonna say something like a scramble. Tell me how many people grown that's gonna eat at the table with me and we're gonna do it over easy. Now, with that being said, let me just take this time to say, thank you for watching this video. Don't forget to like, smash that subscribe button and tell everybody out there, check this out. There's a channel out here to simplify these recipes and taking the mystery out of cooking. And guess what, folks? I'm finna hurry up. I'm finna walk out, let it in, and I'm coming back, snap my picture and I'm about to eat. Peace.


Hi, I'm Sebastian from coccy.nl. Today we've been making anaglyphs. Anaglyphs are the type of 3D photos that you can watch with the colored glasses like this, with the blue and the red glasses. So we make this little setup. You can see that we have two webcams here, side by side. So we capture two images at the same time to get the 3D effect. And we have some everyday objects. So like a pen here and we have a coffee cup at that time, those kind of objects.  And some lamps, of course, to get a nice lighting. And we attach the webcams to the laptop, as you see here. So here you can see, if you zoom in a little bit, you can see the 3D image. So it doesn't look very 3D right now, but if you shift the red channel a little bit, you can see that it's a 3D image, right? So if you watch it with a pair of goggles like this, and you tweak it just right, you get a very nice 3D effect. So that's what we've been doing today. Thank you.


Everybody forced here ripping 2022 select football hobby 12 box full case number 11 that ran of the visions can be just a sec. I'm gonna show you the results there. They are Let's go ahead and get started Thank you. Thank you for joining find them anytime late sports cards calm and in the results tab on the results tab there And just want to go in the Jersey case next Another Jersey case and there's dual case eminence and flawless if we don't get eminence of flawless filled up I know it's got like 21 left. It'll just go. We'll reschedule for tomorrow and try to get it filled then Need to give Sam a chance to pull some heat out of those I think I think I've done all of them all the dual cases, you know Kid deserves a chance I guess Try to try to keep up All right, let's see if we can match the heat we pulled in the last case Silver rookie concourse Devon Lloyd AFC South. That's a nice tie-dye Lamar Jackson 16 of 25 AFC North premiere level Quick someone tell Sam Wanted to see that I what I pulled and no way Silver rookie Abner NFC North you just jealous Joe's are no Joe's lurking Silver rookie sweet level is Geron Harmon AFC West Nice a tricolor sauce to 149 AFC East rookie sweet level sweet Silver DAC a NFC East there Damien Pierce Gotta Matt. Oh, you got a card stand card real early It's I cut coming up to 25 Tyrion Davis price tie-dye rookie Otto NFC West Purple Jamal rookie concourse NFC North. That's nice to 75 and a Taylor Heinecke Otto to 75 NFC East It's healer Heinecke I'm gonna go home and eat some salt and vinegar chips. That's how I'm gonna do love Just like man thinking about them chips Ricky concourse blue Devon Lloyd AFC South to 199 got silver to a AFC East That's how we talked about food. It's been a while Since those a one potato chips Oh I'm gonna try it. I might get it tomorrow, dude. Let me know silver snap shots Josh Allen I might actually just make some Mac like a talent some for real Mac cheese That's the best way to silver breeze haul AFC East We'll go to like a legit barbecue place bring my sneaks and a one sauce in there So 99 is Jersey Trayvon digs NFC East Ricky silver concourse Kate Odden NFC South AFC North Jamar Chase silver Brock Purdy field-level base That's not pretty I might be down. Let's go. I know he's there. I might be harder There's a picket followed by gold tea Higgins a FC North That is a sweet card 10 to 10 club level T Herbie you got a silver Mijai Sanders Ricky for the NFC West We'll get the T mag for you AFC North Xrc in the first box silver dulcet Ricky field level And it is quarterback to AFC South CJ Stroud Oh Yeah a one congrats So the Texans AFC South CJ Stroud Xrc. I just hit the camera That's a fantastic box orange Ricky concourse NFC South Trevor Penning That's out of 49 and to 99 is Hedrick Wilson jr. Auto AFC East Who the Dolphin should trade Tyra kill of the Patriots? No got silver fuel in NFC North. Yeah Yeah, give us him and Rams he got silver Michael Parsons NFC East It's a Petrie field level rookie. I like the Patriots to be watchable this year Try color rookie Berks for the AFC East So AFC South to 49 of those AFC South Berks, of course Silver Rashad white NFC South rookie my home's base Isaiah Spiller to 99 rookie Jersey Auto AFC West Mathis another Xrc. Oh boy getting them out getting them early in this case early and often Silver Josh Jacobs inserts over Devon Bush AFC North And we're going defense three that's gonna be Raiders AFC West Tyree Wilson Card of 520 AFC West Tyree Wilson. Here we go. Haven't pulled that one yet. I hit my bingo card Blue rookie Logan Wilson NFC South to 149 got a silver NFC or AFC South Jonathan Taylor We should go play bingo sometime Kenneth Walker the third Dude, you got to be ready though. I gotta get the pens like Silver Pierce Ricky Rock party. Oh, we're going we're doing bingo night some night. We should do a bingo night at the shop We should go I'm down Conquers Red Rookie Trevor Penning NFC South to 99 Silver Keons anger, is it good? Yeah Like 10 bucks To 75 Chase Claypool in the Jersey card NFC North Silver borough AFC North Can you pick it? Silver Kurt Warner NFC West Dobbs field level Yes, that's crazy man, you got a white field level Kirk Cousins NFC South to 35. I remember you tell me about this Yeah, I can imagine silver NFC West McCaffrey early. I'll probably be here on Thursday. I'll probably be here for the Wild Thursday Crap that ain't gonna work I don't even know I wouldn't I wouldn't count on that. There's no way It's incredible How many people huh? Yeah Silver Conquers Rookie Sting Lee for the AFC South Should you break break or bingo neon icons decked silver NFC East he Higgins AFC North Silver sauce base There's a redemption here for Damian Pierce AFC South Ricky memorabilia signature blue prism AFC South Damian Pierce Light blue rookie is Tyler Smith NFC East at 99 silver rookie concourse Lewis seen for the NFC North Minka Fitzpatrick gold patch AFC North To have 10 gold patch Minka only color match Silver concourse to a AFC East Yeah, yeah, stuff's fire bang Used to go all the time for all you can eat wings And Do my best to get my money's worth. Oh, yeah Red sweet level Joe burrow AFC North It's a 49 nice burrow there. I've got a Watson sweet level silver Gabriel Davis AFC East Tri-color concourse Donovan Wilson NFC East 249 Silver Dylan Parham zebra feel level to rel Edmunds AFC North my zebra short print Rail Edmunds now we get a silver field level of Tyree kill AFC East. Come on. Get rid of the Patriots Take all the good dolphins got my homes Bekette a blue rookie for Darian Mathis NFC East Out of 149 and to 99 Tyree kill AFC East Jersey auto That's the one that's who we need Get him from Mac D hop and Tyree kill we're gonna survival Well, not maybe not. Yeah, I think it was I think it was had a visit plan Could be interesting silver rookie concourse is Jermaine Johnson the second AFC East Desmond Ritter Silver sweet level rookie Jalen Tobart NFC East Olavé base Try color Darius Layton Vaughn.  Got try color Darius Layton to 75 NFC East silver concourse Sam Darman NFC South.  I think I might get some crumble tomorrow. That's a good idea Dude last week was last week was absolute fire the lemonade cookie.  Yeah cookies are huge Got Romeo and Dobson 99 on the rookie Jersey auto for the NFC North ruin rookie concourse scholar Thompson AFC East Number to 149 Silver Jamar Chase concourse Vaughn, how are the rest of the crumble cookies this week before we get into the this or that? Silver Modrae Stephenson field level AFC East because you said the I Forget which one you said was pretty was like decent silver concourse rookie quay Walker NFC North Silver Sensation Jonathan Taylor AFC South Silver rookie is a Luke Godeky or got a key the NFC South Don't switch field level rookie tri-color rookie Haskins AFC South as to what 99 Premier level Silver to Sean Watson AFC North I'm gonna get them all the Reese's one. I'm interested in the Reese's one could like really really Be amazing or I feel like kind of disappoint kind of fall short Anything Reese is just like you you put branding on something. It's like oh boy expectations are high now Because you've all had like really good Reese's like peanut butter pie or something like that before Don't get on the trash list crumble Silver Nick Chubb AFC North Don't do it Blue rookie is stoop Connor AFC South to 99 and Eli Mitchell to 49 on the maroon auto NFC West Silver concourse Dak NFC East Kenny Pickett Purple rookie Davis Price NFC West 75 Silver concourse rookie Kate Odden NFC South butter peanut butter blossoms What's that? 49 sky more rookie Jersey AFC West Is that like a buck eye those are fire? Silver Justin Herbert AFC West Do we eat on this? I'm gonna spend my day cooking and like baking things and not actually doing like PSA gotta work Try color NFC's to 249 Dak Silver Cam Jergens NFC East, I don't know how much I don't think I have a ton the list But I didn't take a few hours and go through cards and Smoothier milkshake can only keep one. I think honestly. I'd probably keep smoothie because I feel like I've had more smoothies In my life than a milkshake The problem is is like when you're craving a milkshake. It's like Really Yeah, it's it's it's a it's a tough one I'm trying to think of some of the best milkshake some of the best smoothies I've had That sounds fire Son Haskins the 99 rookie light blue AFC South Silver concourse rookie Trevor Penning NFC South. Yeah, I'm thinking about this sauce Silverfield level Kelsey AFC West Milkshake or milkshake See Higgins at 25 on the tie-dye patch AFC North Silver key Taylor Britt AFC North That's my thing is I also haven't had a milkshake in forever Yeah, if I do ever get like ice cream, I just get like ice cream Yeah, so for concourse Keenan Allen AFC West do we keep every time Sean and I go on about the damn ice cream sandwiches The Mayfield at Publix is Bogo It's like the cookies, but it has the chocolate chips on the ice cream around it, too. That's Bogo right now.  I kept walking now I'm thinking out. I think that it sunk its teeth into me now I got to go back and get it I got him maroon Damian Pierce the 149 AFC South Truth be told the Publix is open on my way home tonight. I'd probably stop and get some yeah Spread dude, and I'm glad I never late at night because that's my most vulnerable I'd stop in there, and I'd be buying like fried chicken. I'd be buying everything Silver Moppa. Yeah, that would be dangerous Yeah, I'd be grabbing like Oreos and deli cookies or bakery cookies all this stuff, man Beers are coming to be a beer. I'll try color easy comma to 249 AFC East Always make bad decisions over juju Mostly it's with like food and stuff.  I stream sammys or fire I feel that Blake. I feel that my daughter's blue picket rookie concours. I used to 199 AFC North and right behind it four of five green auto NFC was Zach Erts Nice Erts, and then there's a London base Man that sounds good. I need to go to a place like that conquer silver John the Taylor AFC South There's probably a sweets place around here that does something like that Costs like eight bucks for the sandwich, but worth it Sweet shots Jordan Boyer AFC East into 35. There's certain things that you kind of pay like anything for And it's like a beard a theme park You'd pretty much pay anything Concert yeah conquer silver Donovan Wilson NFC East They know that and that's why they're priced like they are because they know we're gonna get one Silver Sensation Jefferson NFC North Silver Sutton Broncos AFC West Like people are gonna get trashed anyway. We may as well make money deal with these jerks Yeah, I don't need a lot of smoothies either. I'm just trying to think in my head like maybe it's more vulnerable like maybe Maybe it's reversal not vulnerable It's reversal to have a smoothie because like it's also healthier So you could You know, I'm gonna get a smoothie tomorrow. I'm gonna get chips tomorrow I'm gonna get so much stuff that we're talking about tonight tomorrow a one steak sauce Mets you to 35 on the white rookie auto AFC South Nice.   I'm going a one milkshake. Yeah Sweet in the end.  Yeah got silver Josh Allen AFC East Toothpaste moisturizer Blue sweet level Jamar Chase AFC North You look like a crawl to the mud slivered Jared Goff Yeah, Shane gets it you were you weren't here earlier we were going on on about the a1 Zebra Stefan dig snapshots AFC East Grads on that one silver Brock party on the club level NFC West With sour cream. Yes Shay. Oh man. I don't even need a smoothie. Just give me that Not in town purple working concourse to 75 NFC South Trevor Penning. I think we should just be a surprise They want government is 75 Jersey auto for the NFC North I Need to spend so much money on public smart just random stuff that we've been talking about tonight Silver concourse rookie James Williams NFC North, you know, we're talking about milkshakes and through these I don't even own a blender. I got a blender somewhere Right, so try color to 199 AFC West Orlando Brown See if I bought a blender I would go I would use it every day for like a week That's silver Shakir No, I don't but yeah, tell me Silver sweet shot scene brown and MC North Condiments water So I'm married so I have stuff in the fridge We're bad though, like there's certain weeks will go without we'll go like two weeks I'll do a grocery shopping and just order order meals like delivered or whatever go pick it up because it's cheaper that way a lot I'm gonna go buy two rib-eyes at the store. It's gonna be like 25 bucks like Easy, yeah, and you're gonna buy other stuff too. Like I don't even I don't try to go to the grocery store anymore Cuz it's more expensive to do that than to just order some food and cost and have no time have no time wasting Ricky Jersey auto berks to 199 AFC South It's a good move Light blue Tom Brady NFC South number 299 or you grab like a pizza or something Last year forever you go NFC South and Brady silver rookie concourse Berks AFC South. Yeah, my fridge We have some leftovers in there right now. Oh, I do have some Publix trades latechase in there and some Publix Cheesecake with strawberries in there. Oh boy. That might be gone. I might be gone by A few hours silverfield level deck Not the best cheesecake, but still really good, you know, I mean When it's late at night, it's really good crazy crazy. Come on guys fanatics under wraps Just one left fanatics under wraps link is in chat Hey one on five bologna sandwiches. I do it. Sounds good to me. I do it. I love 75 Tyler Algear Jersey card rookie for the NFC South There's some peeling on the back of this Algear. I'm gonna send a boxer rapper to the NFC South on this one I'll say already have one silver concourse take one Silver key concourse Nick Bonito AFC West That's pretty sweet, I have no problem with that what so I had bandwagon so hard for the Jaguars Concourse maroon Cameron Jordan to 1 to 49 I need to get a Jaguars hat actually silver Mahomes AFC West Just keeping the repertoire my first non like You know Team that I'm a fan of hat from Lane that that Raptors Silver same brown NFC North. I'll be down with that because it's the Pats don't have a chance I wouldn't say never but the path is a lot more rigorous Yeah rookie Malcolm Rodriguez sweet level tie-dye It's a sweet one to 25 NFC North and that's how the lock it auto Nice lock at AFC or NFC West is 75 My fridge got Some berries eggs Silver key concourse Romeo Dobbs NFC North was all this stuff yogurt Don't eat those eggs Eggs berries beer obviously that's the got purple rookie and egg barry for the NFC North 75 a good amount of beer like eight different kinds to work concourse over scholar Thompson. He's yeah, he's happy Silver snap shots Jefferson NFC North silver Lawrence Jags Try color concourse Bobby Wagner NFC West to 49 silver epic at CA rookie Fanatics under wraps Authentic baseball jerseys pulled mookie earlier pulled Nolan Ryan strikeout king inscribed. Oh sold out. Never mind Guess we chewed out the other one too Got try color rookie key on to increment NFC West out of 199 Silver Ramsey NFC West Brock Purdy neon icons silver say one NFC East Try color Juergens NFC East rookie The Premier level to 199 Silver and matchy premier level rookie AFC South Silver timbadoe sweet level rookie NFC East home snapshots to 199 Taekwondo and rookie auto AFC East XRC Silver Donald Field level NFC South XRC is tight end to Tight end to number 517 that Sam Laporta NFC North Lions Sam Laporta NFC North and Cade Laporta. Oh, it's only they only have two tight ends, right? Yeah, only two tight ends XRC's Blue rookie concourse Garrett Wilson AFC East That's out of 199 and a 25 Elijah Moore tie-dye auto AFC East Concourse blue rookie McCreary AFC South that one's out of two of 199 Silver makeup. It's Patrick AFC North Taylor Garrett Wilson switch sweet level sensations McCaffrey silver judon That checklist says it's a It's Laporta When can Cade Yeah, Laporta was drafted the pick before Michael Mayer Yep, no the checklist is right to 99 is sparks rookie Jersey a con quo AFC South silver to Sean Watson silver concourse Baker Mayfield NFC West Try color rookie sweet levels George Pickens nice one AFC North this one's to 149 Silver concourse rookie bonito. I Was reading the checklist. I didn't know the top my head if you were to ask me I probably would have said mayor because that's the name. I know more sauce 75 sauce rookie Jersey Auto AFC East Light blue rookie Jelani Woods for the AFC AFC South to 99 Silver Russell Wilson concourse AFC West Ritter Silver Miles Garrett sweet level AFC North Silver concourse Bobby Wagner NFC West a Chaco rookie field level AFC West Concourse maroon Baker Mayfield NFC West that one's out of 149 silver tibodeaux rookie Premier level NFC East Silver field level Tana Hill AFC South London rookie Have to go try a Smoothie tomorrow and see if I can do it for that that and only that forever What's that try a smoothie tomorrow? I'm gonna know what maybe I could do this. Maybe I couldn't to 149 blue Premier level Marlin Humphrey AFC North and Gold with 10 is Alan Robinson auto for the NFC West I'm thinking milkshake. Oh, so I'm gonna enjoy something. It's gonna be that yeah Silver concourse Cal pits NFC South there are some people that would for sure say Smoothie no question. No, like Lane Got try color field level Marquise Brown NFC West 75 Silver concourse rookie Nicobi Dean NFC East Zappy to 75 Ricky Jersey AFC East silver concourse rookie Calvin Austin a third AFC North Silver snap shots Lawrence AFC South and a silver AJ Dylan NFC North Come on do some big cards here Got magazine to use rookie concourse try color quay Walker NFC North out of 249 and silver Jerry Judy AFC West That's still going right? Yeah Still going on a personal slide over there Pickings the 25 tie-dye rookie auto AFC North 21 of 25 got Claypool Congrats AFC North I'll do Blue concourse Justin Fields and NFC North that one's out of 199 silver concourse rookie a Cuono NFC South Silver Sensation's AFC West is Herbert silver Jacobs AFC West The 75 Josh Allen Jersey card AFC East Rookie concourse over McBride NFC West Silver sweet level Mahomes AFC West Yeah, the tie-dye forces with me today Any more in a tie-dye shirt or one yesterday though Try color Ricky's a mere white AFC West to 199 Silver Logan Hall Blake just made a picture of he just got crumble It's pretty fire Silver London on the phenomenon NFC South with an a NFC South of Keem Hicks blue concourse rookie K-Dot and NFC South K-Dot numbered to 199 Michael Vick to 199 Jersey Auto NFC South concourse silver Christian Harris for the AFC South I needed a bleach tie-dye one of my late insurers That's what I need to do. God try color Jalen Hertz rookie NFC East to 199 Silver concourse rookie Cole strange for the AFC East Try color is rookie Reggie Gilliam for the bills Sweet level to 149 AFC East silver rookie color Gordon NFC North Silver rookie concourse Watson NFC North. All right last couple boxes And we got jerseys Got Kenny Pickett. Oh, man. Y'all see that Gold rookie auto 10 of 10 What an absolute monster hits for Sean M On a oh Shoot that is a big hit. That might be the biggest hit tonight He's even got the two gloves on Jordan Brooks NFC West visionary Short print there Silver TJ Watt AFC North and a Brock pretty base Bailey's happy blue sweet level So 99 rookie for the AFC East and a Super Bowl auto Niners NFC West John Taylor I was a quick quick pull for pickings Only up there for a bit Holy cow silver concourse Dak Drake London Love a sweet level tri-color Devonte Adams AFC West to 149 Silver rookie Kenan Green AFC South Silver sensations Herbert AFC West silver Dante Foreman NFC South you rather have a number eight of ten One of ten or ten of ten. I don't think it matters a whole lot Rookie concourse purple Nick Bonito to 75 See West silver dianthe Johnson Silver sweet level Durbin James AFC West Now Lamar says I couldn't have I couldn't have two Steelers up there Not allowed Saw scarter 99 rookie Jersey card AFC East If you if you got you don't even get to you have to be a playoff team if you're gonna get to up there Silver Jamar chase the FC North Playoff team Sadly couldn't even put two Patriots cards up there Silver concourse Herbert AFC West They made the play They made they technically made it Wow a sweet level tie-dye AFC East Josh Allen 18 at 25 idea Ryan rookie silver K your case K-pop is Conquest Ricky blue cold It's a one ninety nine AFC's might be wrong chat rookie concourse silver is K dot NFC South Maybe someone knows the answer that question. They really answer that question. I can't help Ryan in this and with this one I'll listen to K-pop. Am I missing out is K-pop is K-pop. What's it? It seems very I Don't know what to describe it as Every like Yeah, but it's also like not at all any more in these I Can't listen to K-pop. I listen to everything that I've I don't say any music. I listen everything from like the 90s Got redemption breeze hull AFC East rookie signature memorabilia prism How's that a red card for me? Oh For saying that Two Steelers can't be up here Like says he likes K-pop rookie blue is Tyler Smith NFC East to 149 silver Justin Herbert AFC West All right Blake give me one song to listen to I Will give it one chance on my way home. It'd be the first thing I put on I won't Tie-dye rookie Berks AFC South. Yeah, Sean's making sure he knows that he making you guys know that he won't do it Dude, I'm gonna take Sean to a bar. I'm just gonna play K-pop They don't have it you've never heard of Blake sliver concourse lock it NFC West Thank you, I thought Blake was serious. I can't pick it see I would trust Blake with with one chance There's no I won't trust anybody else in chat right now the rookie concourse silver Devon Lloyd AFC sound tree folding I mean, it's just American pop. It's just Korean. It's the same stuff Try color hunter Renfro. AFC West to 149 Kenneth Walker the third Yeah, that's yeah That was my reaction. It's pretty normal. It's like all right If you're saying it Ricky's silver or conco. My reaction was not the same as for Sean tell me Sean is not open to new things. He just Just does what he knows Yeah, you can't be the lion when he's in the cage. No, that's number one you also know that Don't be lying in the cage old dog new tricks can't do that Purple Deontay Johnson AFC north What's going on in this pack two numbered cards? Okay, I can separate them here. There we go 75 Julio Jones NFC south to 149 and a Willie galt on the auto for the NFC north The galt Super Bowl auto the person that brought up K-pop cause it caused a commotion as it says One word Silver Allen Robinson Mom's I'm telling you had to be like wrong chat or something. They have like multiple streams up or something like that How are the Hornets worth three billion is because they're just NBA team They're just yeah, they're just they're just doing that because they're an NBA team silver David Bell that has to be it Right, so what are the magic worth? We actually have a young star And we're in our land though Vaughn how much did uh, oh look at that Romeo and Dom's tight I feel love a rookie NFC north. No, I have not Blake. I don't think I would ever do that. Oh my god. That's diabetes silver trouble I think Blake you're young. I Can't do that. There's no way man.  You can probably burn through it way quicker than I could Like it would just sit with me for like days. I'm like It's a color to 199 Kyler Maria a couple gallons 90 gallons Silver Kyler Murray He bought them for 275 million.  That's what I'm saying. That was not that long ago either That was like what I was like what 20 years ago.  All right, relics of Berks sauce Josh Allen Bailey zappies Conquo Algier Sanders Higgins on the tie-dye Skymore gold minkip. It's Patrick Chase Claypool and Trayvon digs Vaughn, I'm gonna be sick. I was listening to something on the radio that couldn't believe it NBA grown that much I guess it has. Yeah Quick dude People in the US don't realize like football is growing super fast as much while sports here But I think the NBA is growing the fastest like we're live. It's getting nuts. Yeah, the autos of galt AFC East Reese Hall John Taylor Michael Vic Alan Robinson saw Skarner Elijah Moore Titan to NFC North is La Porta XRC redemption La Porta NFC North Lions Tyguan Thornton Tyler Lockett Traylon Berks David Montgomery John Metschy the third Green Erts Kyle Hamilton Eli Mitchell a Romeo Dobbs Tyree kill AFC South Damien Pierce redemption and AFC West defense three is Tyree Wilson Raiders AFC West on the XRC Isaiah Spiller Cedric Wilson Heineke and Davis Price Tie-dye sweet level Josh Allen AFC East 25 tie-dye auto George Pickens rookie AFC North a rookie concourse blue to 199 picket AFC North AFC South quarterback to XRC prison redemption CJ Stroud Gold Higgins AFC North 10 tie-dye Lamar AFC North 25 and gold rookie auto Kenny Pickett AFC North Sean M Nope. Nope. I'll do it for selects on two fanatics under wraps baseball jerseys


Yeah dear participants, welcome to the course on supply chain digitization. This is jointly being taught by Professor Piyanka Burma, Professor Sushmita Narayana and Professor Devav Brathadas from Indian Institute of Management Mumbai. So, this is lecture 7 of module 3 that is analytics in supply chain management. So, before we proceed for the lecture. So, we will see the summary of last lecture of this module, why demand planning is important. So, in the last lecture we discussed in detail why demand planning is important, then we also discussed the role of AI ML in demand forecasting, specifically in today's context why for demand forecasting we need the AI and ML algorithm. Then we also discussed like what are the various AI ML models are used typically for demand forecasting. So, that is what we discussed in the last lecture. So, in today's lecture we will see a case study and discuss like how AI ML model can be used. In this case specifically we will use one of the ML model and then we will see the result. So, the case goes as follows the demand planning head of a large FMCG company is not happy with the last few quarters forecast. He has been observing a reasonable gap between the actual demand and the demand forecasted by his team. So, as discussed in the last lecture if there is a gap between actual demand and the demand forecasted by his team, then what will happen sometimes you will end up with inventory if the actual demand is less than the predicted demand or you will have a like shortfall. So, if the actual demand is more than the demand you predicted then the customers will not be happy they will not get the desired product. So, they might go to the competitors. So, either you will have like excess inventory at hand or you will end up losing customers. So, that is the result of wrong forecast or if the actual demand is not same to the forecasted demand. So, now with that background so, the manager recently organized a hands on training program on demand forecasting using AI ML for his team. So, he got some idea that in today's context we need to use AI ML algorithm for demand forecasting where customers behaviour are changing, demand patterns are changing very fast. So, therefore, he understood the need of using AI ML for demand forecasting. So, after this training he got some idea that AI ML could be used in like his case as well. So, he is wondering if his team can develop a better demand forecasting model so, that accuracy improves and the gap between actual demand and forecasted demand reduces. So, that is the final aim of any demand planner that if I can reduce the gap between actual demand and forecasted demand. If I can then I am a successful manager because I would be able to plan properly and my inventory holding cost will reduce at the same time my customers also will be happy because they will get the product they want. So, now he immediately asked his team to gather all the relevant data and after debate and discussion with his team he found out the relevant parameters to forecast the demand. So, in this specific FMCG company so, across the country they have many retailers and these are big retailers they place orders to this FMCG company and based on that order they try to fulfil their demand. So, retailers are located in various regions some are located in south some are located in east some west some north so, region wise retailer details we have to capture. Then there is an important parameter balanced credit amount so, that means how much balance credit amount is with them so, this is measured in INR Indian rupees in lakh then location. So, although we are capturing region but within region location is also important whether they are urban the retailer is located in urban area whether the retailer is located in semi urban area whether the retailer is located in rural area and so on. Then we have age that means how old the retailer is if the retailer is very old they will have good influence with the customers customers will know the retailer and they will come and buy the products. Then size of the retail store this is measured in 1000 square feet. So, if the size is bigger more footfall will be there and we are expecting that more demand will come from that specific retailer. Then promotional offer that plays a huge role specifically for FMCG industry if you give some promotional offer that is buy one get one free of course, your demand will go up if you give some discount on a particular product it let us say price discount you are giving. Then obviously, demand will go up then number of holidays also plays a important role if in that particular week along with the Saturday Sunday if you have one more holiday then obviously, customers will go out and buy the products. So, demand might increase during that time period and the last parameter is order quantity. So, from the past data I have from each retailer how much order has come based on the past data I need to find out what would be the order from the particular retailer. So, for each retailer this team of the demand planning team is planning to capture retailer's region retailer's balance credit amount that will be capturing whether they are paying on time or not that means, how much money there they owe to that specific FMCG company location its age the size of the retail store promotional offer number of days. So, we have 1 2 3 4 5 6 7. So, for each retailer I have 7 independent variable and one dependent variable is order quantity. So, I need to find out I need to predict for a specific retailer how much order they will be placing to us if I can predict it properly then I can actually produce them accordingly. So, my production plan will be good and of course, my customers will be happy because whatever quantity they are asking I will be able to give it to them. So, therefore, with these 7 independent variables my job is to predict the order quantity. So, with these 7 independent variables and one dependent variable he and his team collected the data. So, if you look into this data we have 1000 retailer. So, retailer starting with number starting with 0. So, I have 999 that means, 1000 retailers data I have and for each retailer we have their region which region they are from either they are from south or east or west or north. So, I have 4 category of region then for each retailer I have the information balanced credit amount that means, how much money they owe to the FMCG company how much money they are yet to pay back to the FMCG company this is in lakh. Then we have location either it is urban semi urban and or rural then we have age in years like how long this retailer are existed like for how many years they are running the retail shop. Size in 1000 square feet then we have promotional offer 1 0 if the offer was given during that week 1 other way 0 and number of holidays in that week. So, for example, if you see retailer number 1 it is located in east region the balanced credit amount is 12 lakh located in urban area then 6 years old the size of that particular retail store is 2000 square feet and the promotional offer was not given that week and number of all day during that week was only 1. Similarly, if I see 999 retailer number that is actually 1000 retailer the retailer number 1000 in our case region is east balanced credit amount is 24 lakh located in semi urban area 22 years old retail store that means, it has been running for many years the size of the retail store is 57000 square feet huge retail store and the promotional offer was given during that week and in that week I had 2 holidays. So, for each 1000 retailer I have all this 7 parameters and their value then I also have collected their order quantity. So, order quantities are like for retailer number 0 it is 40 retailer number 1 is 0 that means retailer number 0 which is located in south region placed an order of 40 unit retailer number 1 which is located in east region did not place an order during that week retailer number 2 which is located in south region having 11 lakh balance placed an order for 300 units and so on. So, I not only have the values of the 7 independent variables I also have the value of the order quantity now as a manager my job is to predict. So, these are my past data which I have with me. So, using this past data I want to predict or I want to forecast like what will happen in the future. So, these are all past. So, let us say I want to predict if a retailer is located in west region and it is balanced credit amount is 10 lakh and the area is urban area the age 12 years size of the retail store is 8000 square feet and the promotional offer was given during that week and I had 3 holidays during that week. Now I have to predict how much order I will get from that particular retailer that means what will be the demand for the retailer during this week having these characteristics. So, therefore, I need to develop some model which will help me to predict the demand for this particular retailer. Similarly, I have retailers across the country. So, for each and every retailer I have to predict how much order they will be placing to us that means what would be my demand as an FMCG company how much demand I will get from these retailers. If I can predict properly and if my actual demand matches with the predicted demand then nothing like that my inventory holding cost will go down as you have discussed. Similarly, my loss demand cost also go down. Now with that objective in mind the manager in this case came up with the idea of regress entry and develop the model. So, there are many IML models, but their team decided that they will develop a regress entry model accordingly. They started working on that and after developing the model they got the output and the output of the prediction model is presented in the next slide. So, now we will take some time to explain this output and then once the output is explained we will go back and try to explain like how this model has been developed. So, initially I am like presenting the output to you, but how this model has come how this model has been developed what is the background algorithm all will be explaining it after some time. So, first let us focus on their model. So, this is a regress entry model they have developed and if I see I had initially 1000 observation. So, I am using 700 observation for training purpose that is 70 percent and rest 30 percent data which is 300 observation I am keeping it aside for testing the model. So, now with this 700 observation if I have to predict what is the demand of each retailer what is the demand of each retailer then how can I do it. So, if I see in the node 0 I have all the 700 observation and the average of this 700 order quantity is 2270. So, that means if I do not have any information if you randomly pick any retailer and ask me what would be the demand of this retailer I will say 2270. So, how did I get 2270 is nothing, but the average of all 700 retailers order quantity that is simple y bar. So, if I just write it down over here. So, this is nothing, but simple y bar. So, what is y y is nothing, but order quantity. So, I have order quantity of 700 retailers I have taken the simple average of it that is what my best prediction because I do not know any other information. Now, in the second step I am splitting node 0 in two parts using one of the independent variable that is size of the store. So, now I am giving you more information. So, if size of the store is less than equal to 30.5000 square feet then my demand would be 1902. If the size of the store is more than 30.5000 square feet then my demand is 4829. Now, if I compare node 0 versus node 1 and node 2 you will see the difference. So, in node 0 I do not have any information any random retailer you tell me the demand would be 2270 the predicted demand would be 2270 because I do not know any characteristic of the retailer. But as soon as you give me some information some additional information for the retailer in this case I am giving you the information of the size of the store. If size of the store is more than 30.5000 square feet that is size of the store is large then I am predicting that demand is also high. So, they I am expecting that the retailers with more than 30.5000 square feet area would place an order of 4829 that is my predicted demand. If the size of the store is less specifically less than or equal to 30.5000 square feet then I would expect that the retailer would place an order of 1902 units. So, now if I compare node 0 versus node 1 and node 2 you see node 0 my predicted value for all 700 retailers were 2270. But as soon as you give me the information that size of the store is less than equal to 30.5000 square feet I am telling you no demand is predicted demand is not 2270 it is 1902 it has been updated. Similarly, if you give me the information that the size of the store is more than 30.5000 square feet then I will tell that actually the predicted demand is not 2270 the predicted demand would be 4829 units. And how many observations I have I have 612 observations which are having size less than equal to 30.5000 square feet and I have 88 observations which is 100 percent of 700 for which the size of the retail store is more than 30.5000 square feet. Now, the question is can I improvise this prediction can I get better prediction yes you can get better prediction if you give me more information. So, the more information can come like this. So, now in node 1 I have the information that the size of the store is less than equal to 30.5000 square feet. Now, I have 612 observations of that category. Now, can I split this node further. So, I can split this node further using an independent variable called promotion. So, promotion has 2 value 01 if promotion is 0 that means no promotional offer was given during that period if promotion equal to 1 a particular promotional offer was given to the customers. And if we know if promotional offer is given to the customers the demand will go up and that is what exactly you can see in this data also. Now, we split node 1 using the independent variable promotion if you see promotion equal to 0 the demand predicted is 943 a promotion equal to 1 demand predicted is 2360. You can see the demand has increased the predicted value of the demand has increased. So, if I am at node 1 then for all 612 observations I am predicting the demand is 1902, but as soon as you give me the information that the size is less than equal to 30.5 plus the promotional offer was given to that given by that retailer then my demand would increase to 2360 and that is how the demand and the predicted demand value is improvised. Similarly, I can split the node 2 using another independent variable called age. Now, in node 2 I have 88 observations and for all 88 observations I am predicting that my demand is 4829. So, it is relatively high compared to node 1 because node 2 the size of the retail store is high if size is high more footfall will come and obviously, I will predict the demand also will be high. So, therefore, if you compare node 1 and node 2, node 2 average demand is high and that is why the predicted demand is also high. Now, if I use age and split node 2 I am using the age value 17.5. So, if a retail store is having more than 30.5000 square feet area and it is more than 17.5 years old then the predicted demand is 8227. Can you see like the predicted demand jumped from 4829 to 8227, why? Because the size of the store is large as well as its old store. So, many customers knows it old means more than 17.5 years customer knows it they go to this retail store buy it. So, obviously, old store having huge area so demand is also high. So, I would expect that this kind of retailers would place a large order to me and in this case I am predicting that demand would be 8227. Similarly, if I go to the left hand side here in this case I have size of the retail store is more than 30.5000 square foot, but like the store is relatively new age is less than equal to 17.5 years my predicted demand is 2887. So, now if I compare node 0 so node 0 I have 700 observation all 700 training data I have and the predicted value is 2270. So, irrespective of any characteristic if you randomly pick any retailer and ask me what would be the demand I would say 2270. Obviously, this demand will have lot of error compared to actual demand because I am not using any characteristic of that particular retailer. So, therefore, we use like smart criteria and splitted the node. So, node 0 is splitted into node 1 node 2 then node 1 is further splitted into node 3 and 4 and node 2 is further splitted into node 5 and 6. Now, this 700 observations which are at node 0 splitted into 4 part node 3 which is having 198 observation that is 28 percent of the data node 4 414 observation which is having 59 percent of the data node 5 56 observation 8 percent of the data node 6 32 observation 5 percent of the data. So, if you sum it up it would be 700 observation. So, this 700 observation which are at node 0 splitted into 4 node or I can say 4 clusters node 3 1 cluster node 4 1 cluster node 5 1 cluster node 6 1 cluster. So, all the retailers which are falling into node 3 for those retailers my predicted demand is 943 all the retailers which are falling into node 4. So, who are those retailers who will fall into node 4 the retailers whose size is less than equal to 30.5 thousand square feet and they are giving promotional offer during that week and the demand is 236 that is predicted demand. Similarly, all the retailers who are into node 5 I would predict the demand is 2887 all the retailers who are into node 6 I would predict the demand is 8227. So, who are the retailers can you say who are the retailers who are into node 6. So, the retailers are those whose size is more than 30.5 thousand square feet and age is more than 17.5. So, now I have used 3 independent variable first size of the store then second promotional offer whether promotional offer or even by the retailer or not and third age of the store how long they are into the existence. So, using these 3 variable I can predict the demand or I can predict the order quantity by the retailer. If I increase the depth of the decision tree if I further split node 3 node 4 node 5 then obviously, my depth of the decision tree will increase and my prediction will be much better. Suppose, this is the decision tree or the regression tree to be specific which you have built and based on this regression tree you want to predict. So, you have a retailer let us retailer A which is located in west part of the country balance credit balance credit amount is 10 lakh rupees they are located in urban area age of the retail store is 12 years old the size is 8000 square feet and the promotional offer was given during that time period I have 3 holidays during that week. Then the question is what would be my expected demand like how much order this particular retailer that is retailer A would place to me. Can you predict this data or the demand based on this decision tree yes I can. So, first I have to see the size of the store size of the store is 8 that means I am here. So, I am going into node 1 because in my case retailer A size is 8000 square feet. So, node 1 is cluster of those retailers whose size is less than equal to 30.5000 square feet. Now, next I have to see promotion was given promotion value 1. So, I will move to this part. So, I mean node 4 so node 4 predicts the demand is 2360. So, what would be this value? So, this value will be 2360. So, my predicted demand for this retailer is 2360. So, that is how for any retailer across the country using these 3 parameter size of the store promotion and age you can predict what would be the demand of those retailers. So, now if I summarize I have 4 node each like node 3 node 4 node 5 node 6 given the data of any retailer it will fall either in node 3 or node 4 or node 5 or node 6 and based on that I can predict. So, if I just summarize I can create a business rules out of it the first business rule would be the size of the store less than equal to 30.5000 square feet promotion is 0 demand is 943. So, that is what we have written size of the store that less than 30.5000 square feet promotion is 0 predicted value is 943 matching. Now next size of the store less than equal to 30.5000 square feet promotion was given for those kind of retailer demand is 2360. Size of the store less than 30.5000 square feet promotion was given demand is 2360. Then next size of the store more than 30.5000 square feet age less than equal to 17.5 years demand is 2887 with this characteristic. Now we have last criteria size more than 30.5000 square feet age more than 17.5 and then demand is 8227 and I have this particular characteristics. So, I have four value of the predicted demand depending upon the size of the retail store and the promotional offer and the age of the retail store I can predict the demand of each of this retailer and then I have the for that prediction also which we discussed in classification tree. So, for first predicted demand 943 as the support of 28 percent. So, how do you decide support? Support means how much observation you have. So, in node 4 I have 28 percent observation in node 3 I have 28 percent observation in node 4 I have 59 percent node 5 8 percent node 6 5 percent. So, that is what my supporter if support is high if support is high specifically for these two node node 3 and 4 in my prediction I will have more accuracy that is what this support says. So, in the next class we will see how you can also build the similar kind of decision tree on your own. So, thank you see you in the next lecture.


No relaxing that's the that's the theme of December 2018 yeah we did too many too many there's no relaxing this has been such a stressful time for both Jared and I work wise and to be honest I wouldn't have it any other way because it's made me fall in love with you and see you as a partner in such a beautiful meaningful way yeah do you feel that way about me I do feel that way but but I've always felt that way before the busyness came in always gotta one up somebody okay and I'm not saying it like that I'll just tell you the truth you want me to just oh yeah just this month you know I just feel it's just like the truth like I feel like ever since I met you you've pushed me in and and put me in positions to grow that I've never ever touched territories that that you've got me into I've never got to to get to know my man side I feel like me meeting you put me in I'm gonna cry baby you did help me a lot and it's just I can't continue to take these off okay this video is sponsored by Squarespace honestly this is the go-to place for your craft to shine whether you need a domain website or online store make it here fast easy and effortless and make it look stunning with Squarespace the concept for our wedding photos really was born out of what marriage meant to us and it meant the same it meant continuing on what we already have going it meant not making marriage into some kind of accomplishment or final destination but just making it a part of the journey of explaining our love to people and developing in our love in a way that reflects how we feel about each other so the wedding photos are just us doing normal stuff we wanted to symbolize in the wedding photos us doing our everyday routines we and the only thing that was different was us wearing the wedding outfit so yeah to me what that really symbolized is nothing is going to change yes we have a fancier title and in this case fancier outfits on but it's going to be the same work it's going to be the same day to day it's not always going to be some fairy tale fantastical us on the edge of a mountain overlooking a waterfall that's like the lives that we live i was down for those pictures well i don't expect marriage to be like that the only reason i was down for those pictures is because i know the family would want those pictures but i think that's actually a good representation of our relationship because somehow we both got exactly what we wanted and we were no one had to compromise really yeah and i understood and trusted your vision i understood and trusted your leadership and you understood and trusted mine so in that case it makes them even more appropriate but it was it was one of those things where i was like i wonder if these are going to go together like a vibe and they really did it was like amazing and you looked amazing in your dress you look beautiful if we were to do a traditional wedding where she wore this big huge white fluffy dress and then i wore this traditional black tuxedo with a bow tie i think we would have looked goofy up there but i feel like now we look like us we look like a unit we look like what we are we our relationship it's a display of that and i think that kind of going goes into the way we're doing our wedding the whole traditional of it it's like it explains us and it's just like us it's not like them or anybody else and that's what i think that is so special to me about our wedding me i agree with that as well too i think it's a reflection of what we've built and what we value i also think that we also really understood the balance between what was for us and what was for our family yeah and we found a nice healthy compromise in there and so honestly my dress was 100 for my family i just thought that like that was the thing that i knew that they would probably give me the best reaction and it would probably mean the most to them um i am half indian guyades so west indian but descendants from east india and that's a just it's one of those cultural special places that means a lot to my grandma meant a lot to my aunt my mom who is not indian at all is completely fascinated with the culture why was it important for you to have an element of your native culture in your outfit i think there's a couple reasons for that for me uh i i feel like i've only really met my native side i i really only got to know them my dad's side who is the on my black side um i haven't really got to to know a lot of them i met a couple of them i've never been to detroit that's where they're from and the the vest just looked good so so that was just really what it was it was just it just looked good with the outfit and i felt like it was a cool addition first of all super grateful for the photographer amina uh she came through she she handled it she came all the way down from the bay area and i've been a fan of her work for a minute i've been following on instagram she has a really dope like fly on the wall type of uh photography so we just when we saw that we just knew she would be perfect for the job and she really was and we're so grateful for the work that she did in the comment section below i would love to hear from you guys what is one thing that you knew you were going to do for your wedding before you decided who you were going to marry be that the dress be that the photos what's one vision that you have always had in your mind and speaking of visions i want to show you guys the full gamut of the photos that we took uh we're not going to share all these on social media obviously some of them are private some of them just don't need to be shared but you guys we want you to see everything that we got to see and really appreciate the full storyboard that we put together so if you go in the info box below there is a link to our squarespace website we designed this site ourselves we put the photos up there ourselves squarespace of course is how we have been empowered to share our vision in a clean professional organized way we've been working with squarespace now for months yeah and we will continue to do so because they've been an excellent part of to us so in addition to seeing our photos make sure you also go in the info box and see how squarespace can empower you to put your vision out there we built shannon's website from the ground up on squarespace it looks amazing and it took no time thanks to squarespace shannon is now rebooting and rebranding if you're not ready to hand over a fat check to someone else to build your professional site then squarespace is perfect for you host your online store portfolio or legit whatever you want they have a huge selection of templates that cater to whatever you need it's easy to customize and i was able to essentially make any changes i wanted to and i'm no coder go to squarespace.com for a free trial and no you don't even have to give over your credit card information just yet but when you are ready to make it official you can open up a brand new 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