Welcome back. Today, we will discuss sum of a random number of random variables. So far, so last lecture we studied sum of random variables. So, given 2 random variables x and y or given n random variables x 1 through x n, we know how to derive the CDF of x 1 plus x 2 so on till x n, given the joint CDF of these random variables. So today, so in the beginning we will discuss today, the case when you are the number of random variables you are summing is also a random variable. So, you are not summing some small n number of random variables where n is fixed, but the number of terms you are summing is itself a positive integer value random variable. So, let us get started on this, so you have let x i i greater than or equal to 1 be a sequence of independent random variables. So, now here we will only consider the case when these x i's are independent, the dependent case is more complicated. Let n be a positive integer valued random variable with t m f t n of n equal to probability that n is equal to n. So, I should say with CDF f x i that is also known assume that n is dependent of x i's. So, actually what I really mean is that n x 1 x 2 x n they are all independent random variables. Now, you want to consider the sum consider s n is equal to i equals 1 through capital N x i. So, what this means, so let me try to explain what it actually means in terms of the sample space. So, you have a sample space omega f p and you have these random variables x i's defined on the same sample space. Now, this n is also a positive integer valued random variable defined on the same sample space they all live on the same omega f p. So, there is just one underlying source of randomness and little omega realizes and once little omega realizes these x i's of omega will realize as a sequence of real numbers and n of omega will realize as a positive integer some positive integer. So, when omega realizes, so you will sum i equals 1 through n of omega n of omega is now a positive integer x i's of omega. So, you have your sample space omega f p you have some little omega realizing and what I am saying is that. So, x i of omega i greater than or equal to 1 will be a sequence of that particular omega and n of omega will be a realize as some particular some positive integer valued random variable. So, it will be some positive integer for a given omega. So, as when little omega realizes this s n of omega will simply be i equals 1 i equals 1 through n of omega sum x i of omega. So, the number of terms you are summing is also depends on the realization omega it is not a fixed number, but there is only one source of randomness omega is what determines the realization of n as well as the x i's. Now, what you are saying is, so we assume that n and x i's are independent random variables and we know the c d f of the marginal c d f of this x i's is known for each i and also the p m f of n is known. Now, the task is to find first of all I mean you have to make an argument to show that s n is a random variable. We know that some of the fixed number of random variable is a random variable, but you have to make sure that s n is in fact a random variable s capital n and then you have to determine the c d f of s n. So, we proceed as follows. So, we want this right this is the c d f of s n. So, this is what we want to find. So, what we will do, so we will use. So, the realization of n partitions the sample space. So, I am going to look at a partition of the sample space. So, for certain omegas, so this set of omegas for this n may be equal to n of omega may be equal to 1 and for some. So, it takes only positive integer values right. So, this will, so this may correspond to n a of omega equal to 2 and so on right. So, they may be, so if capital n takes only finitely many values the sample space will only have finitely many partitions. If it takes infinitely many values it will have a countable infinity of this partitions correct. So, once I have a partition of the sample space I can invoke law of total probability right that is why I am looking at this. So, is this picture clear. So, all these omegas here will correspond to n of omega equal to 1 and x i of omega will be whatever we do not know right. I am just looking at the partition induced by n. Hence, we can write probability s n less than or equal to x is equal to sum over k equals 1 through infinity. Probability s n less than or equal to x given n is equal to k probability n is equal to k. This is because of the law of total probability right. I am not writing omegas as that everywhere. So, by now you understand that now. So, this is something we know right. Now, this is also something we can figure out because. So, given that n is equal to k this s n is simply equal to s k right which is a deterministic sum right. It is not a sum of random number of random numbers. It is a sum of a deterministic this is like. So, let me write this properly this is equal to k equals 1 through infinity probability s n less than or equal to x given x k. So, maybe I should write s k less than or equal to x given n equals k because I have just put n equals k here because that is what I am conditioning on right times probability n equals k. Now, do we know that. So, between this and this the nice thing is I am now down to a deterministic this on the number of terms is deterministic now it is k small k right and the summation outside is over k. So, can I deal with this now correct. So, because n is independent of all the x i's n is independent of s k see after all what is s k it is only x 1 plus x 2. So, until x k right as s k and you know that n is capital N is independent of your x is. So, capital N given n equal to k. So, these guys the x i's are independent right. So, this is nothing but the unconditional probability right because n is independent. So, this you can write this is because of independent of independent of n n x i I can write sum over k equals 1 through infinity probability. So, this will boil down to the unconditional probability of s k less than or equal to x times probability that n equals k. So, is the step clear this is because of independence great. Now, this is as I said is known to us and is this known to us this will simply be. So, this is the CDF of s k now k is a deterministic number for every term for every k. So, s 1 for example is simply x 1 and we know the CDF of that right s 2 will be x 1 plus x 2 and the CDF of that you can well if it is a you know if you have densities you can convolve right if not you know how to find it right. So, this if your x i's have densities you can convolve and find the densities if they do not have densities you can still find it right. They may be discrete x i's may also be discrete right there is no guarantee that x i's are continuous organizing. So, this is something you know how to find from previous lecture right and then you for each k you have to find it put it in and do the summation right. So, conceptually I mean. So, this does not simplify in full generality, but you know how to do it right given a specific example you will be able to solve it right any questions on this. I can see just in the case of a deterministic number of. So, when the sum is deterministic I said for example that instead of convolving you can use transforms right which makes your life easy. Here too when you use transforms your this simplifies little bit further we will come to that later, but for now all you can do is find this the hard way put it in and sum. Let me do an example which is a very famous example this is the case where x i's are i i d exponential with parameter lambda. So, each x i is exponential parameter lambda independent no there is no I mean there is nothing you can do about this, but you can this is something you know how to find from previous lecture you just plug it in and sum right. So, when you use transforms this formula simplifies a bit we will get to that later x i's are i i d exponential and n is independent of x i's and geometric with parameter p. So, I am summing so you know that. So, when you sum i i d exponentials you get what you do not when you sum exponential you do not get an exponential. So, you get an Erlang right we discuss this right we I think we derived in fact the Erlang to formula explicitly and if you sum n Erlangs you will get n exponentials you get the n th order Erlang right. So, this is a very well known example where you do not sum a fixed number of exponentials you sum a geometric number of exponentials. So, here it turns out the reason I am doing this is it gives you a nice answer it starts out looking messy, but it gives you a nice answer now. So, that is where we are. So, you can apply this rule right. So, you can so s n is equal to sum over i equals 1 through n x i. So, you can think of x i's as being generated as independent i i d exponentials and n is a independent geometric right it takes values in positive integers and you are summing a geometric number of i i d exponentials now what is the distribution of this is the question. So, you can just write probability of s n less than or equal to little x is equal to sum over k equals 1 through infinity probability s k less than or equal to x times probability n is equal to k. Now, we have this we know right this is simply. So, this is equal to what 1 minus p 1 minus p to the k minus 1 times p right and this guy I do not know of the top of my head does anybody remember the c d f of the length I think the p d f looks like the p d f looks like mu to the n x power n minus 1 over n minus 1 factorial e power. So, this is how the p d f looks right and the c d f is the integral of this. So, you put that in and do the summation see what I mean right. So, this is the p d f I think n minus 1 and I think this is right. So, this is the p d f, but you have to put the c d f in here right and you just do the summation it looks messy to begin with, but you can show that this gives you a very nice answer. In fact, what you will get is when you do the summation you get the you can show that s n is exponential with parameter lambda p. So, you sum a geometric number of exponentials you get a another exponential whose parameter is lambda times p and the way you get that is simply do the summation brute force at this point. So, it is nice that if you sum a fixed number of exponentials you get an Erlang which is somewhat messy right. So, this is like this is like small f x this is not the c d f not small f x this is small f s n is not it and from there you have to get this. So, this is a bit messy, but if you sum a geometric number of exponentials you get another exponential. So, that we just showed using brute force now there is a very nice interpretation to this result. You can think of. So, let us say so I mentioned that exponentials are. So, they are the time duration between two successive radioactive emissions right they are exponentials right. So, suppose and the IID exponentials right. So, suppose a radioactive source is emitting particles and they are all IID exponentials with parameter lambda. Now, so you are what you are doing is you are looking at. So, if you look at let us say in time let us say that is my first radioactive emission that is my second that is my third that is my fourth and so on these are radioactive emissions and these are all IID exponentials right. Now, what I am doing is I am summing a geometric number of these right which means I am tossing a coin. So, every time there is an emission I am tossing a coin whose probability of heads is p let us say and I am looking at the duration until the first head shows up every time there is a emission I will toss a coin let us say this gives me tails. So, next time there is a this is give me tails and let us say this give me heads then. So, the number of coin tosses I wait is clearly geometric that is what a geometric is after all and the total time I wait right until I see my first head is S n S capital N right because I am waiting for X 1 plus X 2. So, until X A right X capital N. So, this is the first time. So, let us say if this is where I am starting look at things this is the first time where I see heads with an emission right. So, you can think of this is splitting these alpha particles right. So, maybe your alpha particles are coming out you have a splitter that will send it this way with probability p this way with probability 1 minus p and you are putting a detector over there you are not putting a detector at the source, but you are splitting it and putting a detector over there. So, the first we are saying now that the first time that your detector after the splitter will see an emission is in fact also an exponential understand what I am saying right. So, you can think of this sources. So, if this is your radioactive source all right it is throwing out a bunch of particles and you split it you can think of heads is being splitting up and tails is splitting down right. And instead of putting a detector here and detecting all these emissions you are just putting a detector here and you will only see those emissions which corresponds to getting a head right corresponding to sending here. So, if you look at things here then it look like also exponential according to our result it look like exponential with parameter lambda p, but your original process is like exponential with parameter lambda right is that clear. So, you can give you can build any other story you want right the suppose you are waiting for a taxi and the inter arrival taxi times are exponentials and with probability p each taxi is full you cannot take it right. How long the distribution of how long you wait in the taxi stand is exponential with parameter lambda times 1 minus p right because the probability p is full right understand this. So, this again has to do with the what is known as a Poisson process and what this result essentially says is that if you split if you IID Bernoulli split a Poisson process you get another you get Poisson process also Poisson process being just the process of emissions of alpha particles that clear. So, this is a very well known example. So, in this course we will only discuss the case when capital n is independent of the exercise. So, the number of terms you sum. So, I made this step remember. So, this is only possible if capital n is independent of all the exercise and therefore, independent of S k right, but it is also possible to study the case when capital n depends on the exercise. So, that also has application. So, you may go to a casino and say that I will play a game an IID win or loss game a certain number of times and I will stop playing when my profit is 100 dollars or my loss is 100 dollars or something like that. So, in that case the index where you stop the capital n the number of times you stop is also a function of your previous winnings and losings right in that case. So, that is the case that you will not cover in this course, but it is covered in course of a next semester those case. So, in that situation you cannot make this you cannot go from here to here, but because n will depend on your previous exercise. But, it turns out you can still do it with the more sophisticated technique called using stopping rules you can actually figure that also right even when n is dependent on the exercise in this way, but that is not something we will cover this semester. Any questions? So, this example also. So, right now you have a very dirty way of doing it when we have transforms you will have much cleaner way of doing it, but I suggest you I mean I the reason I did not do it will take 20 minutes for me to do it I will probably make a mistake somewhere I may write n factorial instead of n minus 1 factorial right I did not want to waste class time on that, but I suggest you try it out it is not all the difficult actually it will probably take you 10 15 minutes to do it, but when you use transforms you will see how quicker it how much quicker it is any questions. So, now we will move on to more general transformations. So, far we only looked at maximum minimum some of random variables and some of a random number of random variables. Now, we will look at transformations which are not simply maximum minimum or summations it could be any function of function f of a random variable x or some function of n random variables x 1 through x n just to remind you the picture. So, you have omega f p and you have a random variable x and you have another function f which maps let us say r to r to begin with so if you look at some particular omega this will be x of omega and this will this point will be f of x of omega. And so the overall mapping will be this overall mapping will be f composition x of omega f composition x here we said that f of x or f composition x is a random variable as long as f is a boreal measurable function meaning that the pre measures of boreal sets here must be boreal sets here. And of course, we know that pre measures of boreal sets here are always f measurable right because x is a random variable. So, the problem at hand is we are given some y equals f of x when I write f of x it should be understood as a composition because x is a function remember this is like f composition x of omega. So, y of omega is f composition x of omega but this is the notation I will use not the best of notation, but I will use it. So, the problem at hand is you are given this y equals f of x and I am given the probability law or CDF of x and I want the probability law or CDF of y. So, in actually in principle at least conceptually this problem is quite easy right because let us say I want f y of little y which is the probability that. So, this is the probability of y less than little y less than or equal to little y. So, I am simply considering a semi infinite interval minus infinity y and I am looking at what is the probability of my omega mapping into this correct. Now, I do not see I do not know see I do not quite know what the. So, I am not going to look at the inverse map all the way here what I am going to do is because I know the probability law of x I am just going to look at the inverse map of the semi infinite interval on this real line. So, consider. So, you consider this right f or g already say f. So, f inverse of minus infinity y you consider that right this is the set of all x in r such that f of x is less than or equal to y. So, you look at the pre image of that set here all those x's which map to minus infinity y that clear. So, then it is clear that then. So, consider this consider that set then f y of y is simply equal to p x see this is simply a borel subset of this real line y is that exactly because minus infinity y is a borel set on this real line and f is a borel function. So, it is pre image here must be some borel set correct that borel set we know the probability law before that borel set. So, you can write this as is that clear. So, this is not p this is not the measure on the sample space this is the measure on this real line the probability law of x correct and this is known to us. So, I can write the c d f of y in terms of the probability law of x right. So, conceptually there is no difficulty is this clear in practice depending on how complicated f is this may or may not be easy to do. But conceptually there is no problem for any borel measurable function f and that is it right if you are looking for a formula there is not right this is it right. So, and there may be special cases where you can derive some formula. So, let me just do an example or 2 let x be a Gaussian standard Gaussian and let y equals x square. So, x is the Gaussian standard Gaussian what is the distribution of the square of x that is the question. Now, you know that x takes values in minus infinity infinity y will take values in 0 infinity because it is non negative random variable. So, we proceed as follows. So, we want f y of y equal to probability that y is less than or equal to y which is equal to the probability that x square is less than or equal to little y can you figure that out we know the CDF of x right. So, if you. So, just to remind you. So, the Gaussian sort of f x of little x is not it may be I should use may be I should not use f here I should probably use g because I use f for the p CDF right. So, probably you should put g here everywhere. So, you know that this looks like that right this is your Gaussian and you are looking at the probability that x square is less than or equal to some little y right. Which means your x should lie between minus square root of y and square root of y correct agreed which is simply the area under the bell curve from minus and minus square root of y to square root of y correct. And now you can do some simplification this is this you can write as because of the symmetry you can write it as twice the probability of that bit. So, this you can write as. So, that is my CDF. So, this is like twice 1 over square root of 2 pi integral 0 to square root of y right e power minus x square on 2 d x correct fine. So, that is my CDF if I want my p d f. So, this is. So, this you can in fact this is clearly a differentiable function because it is written like an integral right. So, you can differentiate this to get the density and the density f y of y will be equal to you differentiate that you will get square root 2 pi y e power minus y upon 2 that is it. So, this is for y greater than or equal to 0 this is also for y greater than or equal to 0. So, this is simply by differentiate differentiating this guy. So, this you get x square is y right. So, you have a e power minus y over 2, but you have to also differentiate with respect to y right. So, you get 1 by square root of 2 pi 2 y here the denominator. So, this is just algebra. So, this is called chi square distribution chi square or chi square random variable chi square density. So, if you square a standard Gaussian you get what is known as a chi square distribution that is the p d f. It looks like an exponential, but not quite because there is a 1 by square root of 2 pi here 2 y here 1 by square root of y here. If this were a constant this will be an exponential, but not quite there is a y here right. So, it is not quite an exponential. So, I just did this from first principles right I did not invoke I mean I just essentially I have done this right. I figured out the probability that x square is less than or equal to y f of x is x square right that is exactly what you have done here. So, example 2 let us keep our Gaussian and say y is equal to e power x in this case you will get f y of y is equal to probability that e power x is less than or equal to little y correct. And since, so this is a monotonic function monotonically increasing function. So, this I can write it as probability that x is less than or equal to log y and that is something I know right because I know the. So, this is simply integral minus infinity to log y 1 by square root of 2 pi e power minus x square on 2 dx is correct. And so this is clearly also a continuous unavailable. So, I can differentiate this c d f to get a p d f. So, what will I get I will get instead of x I will get log y square, but I will have a 1 by y sitting here because I have to differentiate log y also right. So, I will get 1 by y square root of 2 pi e power minus log y whole square log y whole square over 2 right that is my density. And this is valid for y bigger than or equal to 0. So, this is called log normal p d f or log normal distribution is there any questions on this. So, if you are given some reasonably nice function like this you can simply look at those x's for which y is less than or equal to y. And then write it in terms of this c d f of x and then leave it there or if you find a density you differentiate if it has a density right that is about it right. So, I think so far I have not said any I have not really derived this is a first principle we are going about it. But it is I have not derived any formula, but it is since in a certain cases where the function is differentiable this function f is differentiable and monotonic you can actually get a explicit formula for the distribution of y in terms of the distribution of x. So, that is something I should probably I will probably do that next class it is called the Jacobian formula. It gives you the it gives you in the case when x is a continuous random variable and f is a differentiable function well actually f is an invertible function I believe. Then you can get an explicit formula for the density of y in terms of the density of x I will derive that for completeness, but I feel that just doing it from first principle there is a very error proof way of doing it. So, we will continue next class.


Hi, come on down. Today is our third annual Denver Police Backpack Caravan. What grade are you in? We are out here with Cronkey Sports, the Denver Police Foundation, and Alpine Bank giving out backpacks to 2,500 students. There you go, thank you. We see the need in our community. This is why officers become law enforcement officers, is to support their community. Middle school? How many? Both in a law enforcement capacity and to meet them where their needs are. And so we recognize there is a need, especially with inflation and the high cost of things, for us to be able to partner with these organizations and provide free backpacks full of school supplies to set these kids up for success in school this year. Do you care about color? Can I get orange? There's a lot of kids out here, a lot of families that are falling upon hard times right now. Cost of living is expensive, you know, things are hard to come by. And so, you know, it's our honor to be able to give back, give these kids what they need to start school on the right foot. Purple, purple, you got it.


So, a lot of people currently are feeling down, demoralized and even depressed because we are in such an unprecedented and just bizarre situation. Like, it really feels like we are living in the dystopian futures that, you know, we read about in sci-fi novels. It feels unreal, almost. And there are some people who feel optimistic because, you know, eventually COVID-19, this pandemic, it's going to go away, right? There's going to be a lot of damage. People are losing loved ones. People are dying. People are losing their jobs. They're losing their material wealth. But at the end of the day, we will one day be able to say that we can put this behind us. But that isn't enough for a lot of people. Like, the 2020 election, it's adding to the bleakness. It's adding to this sense of just desperation because I don't think people fully get it. I wanted to take some time to share a perspective with individuals who think that everything will be peachy keen if we just get Donald Trump out of office. Because for a lot of millennials, a lot of leftists, they don't feel that way. Now, I'm not trying to perpetuate some type of false equivalence between Donald Trump and Joe Biden. There are meaningful differences between these two individuals. But the problem is that, you know, the left had an opportunity to replace the system, possibly, or at least start replacing that system. Get us on the trajectory of social democracy. We had a second chance at electing someone who we felt actually was going to fight for us. Now, Bernie, he's not someone who I felt like was the savior. He, you know, fixed all the problems that the country had. But to me, I felt like he was going to give us a fighting chance. But now with the situation that we're in, there's no sense of, you know, an end in sight, right? Like with COVID-19, we can say, well, at least in a year or two, or like worst case scenario, a couple of years, we'll get past this. But with the current political situation we are in, there's no light at the end of the tunnel. It feels like we're going to keep repeating the same thing over and over every single election cycle. We're going to have a pendulum that swings to a Republican eight years and then a Democrat for another eight years and back and forth. And, you know, so long as we maintain this cycle of neoliberalism, it's not like things stay the same, right? The situation doesn't remain static. The country and the world deteriorates. The situation for normal working people gets exponentially worse with each cycle. So let's just explain why so many young people can't get excited right now about the prospect of getting rid of Donald Trump, even though I think that is important. The problem is that we're not going to undo the mechanisms that led to Donald Trump's rise in the first place. Any competent moral society would never allow a far-right demagogue like Donald Trump to get elected. And it's not like the United States of America is unique here. We're seeing far-right extremism pop up in countries around the world, in Brazil with Jair Bolsonaro in India with Narendra Modi. This is not a unique phenomenon. We're seeing this almost everywhere, right? And it's happening because the global capitalist consensus is failing working people everywhere. So as working people become more desperate around the world, they become more susceptible to radicalization. Sometimes they lurch further to the left. Other times they lurch to the right because a right-wing demagogue will offer them a solution. And that solution is usually bad. It's the immigrants who are causing all of your problems. They're the ones who put you in this economic situation. I'm oversimplifying it. But for an example, because this election will not actually be conducive to a change in the status quo, that's why so many people feel demoralized. So let's just think through why this is. We have a certain set of outcomes. We have two main outcomes, right? And a third possibility, which is highly unlikely, albeit still possible. So outcome number one, Trump is defeated. Joe Biden becomes president. Outcome number two, Joe Biden is defeated. Donald Trump remains president. And in the very unlikely situation, Joe Biden is replaced and steps down. Now, because I feel like that's almost, I don't want to say impossible, but very, very unlikely, we'll talk about that one first. So just on principle, I can't necessarily endorse the idea that Joe Biden should be replaced like we do some type of switcheroo at the convention. Because even if I don't like Joe Biden and I disagree with him on everything, if he got more votes, he got more votes. The only way that I would actually get on board with that situation is if he stepped down, right? And he said, I'm withdrawing my bid for the presidency of the United States. If he did something like that, I would be okay with that. But one, he would never do that. And two, even if he did do that in that best case scenario for the left, it's not going to lead to Bernie Sanders becoming the nominee. Democrats will still fight him tooth and nail. And it will be some other neoliberal who will take his place, getting us right back to square one, right? So I think we can basically rule that situation out. If Democrats switched him with Andrew Cuomo, I think that would be wrong because they're undermining people who voted for Joe Biden. And it's not really going to change the conditions in this country, right? So that doesn't really matter. So what we're really presented with here is two realistic options of what's going to take place that aren't really going to help anyone, right? So if Donald Trump is defeated, that means that we've defeated Donald Trump. Orange man, bad. That's good in and of itself, right? And the best outcome out of a Trump defeat for the left is that Joe Biden can replace Ruth Bader Ginsburg, assuming she's willing to step down. So he can replace Ruth Bader Ginsburg. However, even in that situation, the best situation that we can find ourselves in given the circumstances, I don't think that liberals fully comprehend that that's not enough. The Supreme Court already has a five to four conservative majority. And if Joe Biden is able to replace Ruth Bader Ginsburg, that doesn't change the overall makeup of the court. It's still going to be five to four, meaning that we can still see an overturning of Roe v. Wade.  We will see the dismantling of unions, labor rights. So the fact that the liberal wing of the Democratic Party, which is dominant, is basically hoping for a best case scenario where Joe Biden replaces Ruth Bader Ginsburg. That tells me that they haven't thought this fully through because regardless of who replaces Ruth Bader Ginsburg, and I genuinely hope it is Joe Biden, we still have to fix the Supreme Court. And I don't necessarily know what that entails. Maybe we come up with a court packing plan, but you can't just be satisfied with Joe Biden replacing Ruth Bader Ginsburg. They're going to dismantle our system, give corporations even more power with that five for conservative majority that they currently have, right? Now, of course, we don't want to expand the conservative lead on this court in the event that Justice Roberts wants to flip inside with liberals. We don't want to do that. But at the same time, the status quo as it is, even in that best case scenario is not a good situation. Conservatives are still dominant. And the fact that Democrats aren't actually coming up with an adequate plan to address this is unacceptable to me. It's already an issue. And to me, I worry because Democrats haven't taken this seriously. Now, furthermore, in the event Donald Trump is defeated and Joe Biden is the president, you know, I absolutely expect him to undo some of the things that Donald Trump managed to undo since Obama, right? So you can expect Joe Biden to get us back into the Paris Climate Accord. You can expect Joe Biden to try to restart the Iran deal if Iran would even be willing to come to the table. But the problem with that is any change that we see from Joe Biden, he, you know, gets back into Iran deal. In that best case scenario, he restarts DACA. All of this is most likely going to be changed that takes effect almost exclusively via executive order, which can easily be undone by the next Republican president. So any major legislative accomplishment that he achieves, that has more staying power, right? Republicans, they've been trying to dismantle the Affordable Care Act by death by a thousand cuts, but they can't just undo it with the next Republican administration. But we're not necessarily looking at a situation where Joe Biden is going to come in with a supermajority like Barack Obama. So with Joe Biden as president, you have to understand why the left doesn't feel like everything is going to be peachy keen, because fundamentally we're still going to be stuck in this same situation. And the fact that Joe Biden hasn't really even talked about policy proposals is an issue, right? It's a really big issue. We don't really know where he stands on healthcare. He says that he supports public option, but he came into the White House in 2008 saying he supported a public option and we didn't get a public option. They didn't even propose it. So that's why you've got to understand why young people are so frustrated, because even if liberals get what they want, we're still looking at a really grim situation. Now let's look at the other alternative where Donald Trump is reelected. I think this is probably the likely scenario, although COVID-19 has changed everything and Trump has bungled COVID-19, but his approval rating isn't as bad as it should be, which is astonishing to me. So Donald Trump, he gets another four years, will basically be in the same situation, albeit worse. We've kind of been on this downward trajectory into apocalypse, and that is four more years of absolutely no action when it comes to climate change. And not only that, what little progress we've made, he's going to try to undo it. Where we've made progress at the state level, Trump will try to undo that and challenge states. We're seeing this with his battle with California and their own CO2 emission regulations. So it's going to be bad if Donald Trump is elected. He most likely will be replacing Ruth Bader Ginsburg, which gives conservatives a 6-3 majority. So any hope of maybe Roberts flipping and siding with liberals, that's gone, because it doesn't matter. They have a little bit of a cushion there. They can do what they want. They can repeal Roe V-Wade. They can do anything they want. Republicans can pass whatever legislation, however draconian it may be, and not worry about the Supreme Court overturning it. Whereas even if Bernie Sanders were elected president and he passed Medicare for All, we would have had to worry about them possibly overturning it. It would be a constant battle. So regardless of the outcome of this election cycle, we're not going to be in a good place. Now I will say that, I think objectively speaking, if you are a leftist then Joe Biden will do the least amount of harm. They're both horrible choices, but one is going to cause a little bit less destruction than the other. And you know, there's this line of thinking that, well, what if we just were really organized and we put pressure on Joe Biden? I mean, sure, that's a possibility, but the problem is that if Joe Biden were going to be responsive to the left, don't you think he would be listening to you now when he needs your vote? So if you want to be realistic about the situation, best case scenario, given the set of circumstances we have, is Joe Biden replaces Ruth Bader Ginsburg. But that's it. That's it. Now, you know, another benefit to ousting Donald Trump is that the prospect of war with Iran will largely be diminished. But the problem is that it will be diminished for another four to eight years, because another more competent Republican may come along and do what the party has wanted for decades now, war with Iran. So the problem that the left has with liberals and why the future looks so bleak is because everything that leads to wars, you know, the military industrial complex, everything that leads to economic insecurity, housing insecurity, these systems and institutions are not going to be dismantled and we're not even going to try to dismantle them. And everything that Joe Biden purports to be running on, what we know, you know, his criminal justice reform plan, he's literally undoing the harm that his policies caused in the first place. So the reason why with Bernie Sanders we felt hopeful is because even though we know Bernie Sanders is just one man, we're not expecting a utopian society after Bernie Sanders. But if we can show that social democracy, these types of policies are popular, then that could shift the Overton window more to the left. And that's really, really important. It's important because subsequent administrations in the Democratic Party know they have to adopt that line of thinking of Bernie Sanders if they want to be electable. That's what happened with FDR.  So this wasn't necessarily a guarantee that Bernie would be as popular as FDR. Who knows, right? We didn't have Fox News back during the FDR days. But the point is that we would have been given a fighting shot. But with basically, you know, the coronation of Joe Biden as the nominee and with the prospect of him or Trump winning, that's why the left is so demoralized because fundamentally nothing will change. If Joe Biden beats Donald Trump, things are going to get a little bit better temporarily, right? He'll undo what Trump did temporarily. But everything he undoes will be undone by the next Republican. I mean, anything that Obama did that was good, Trump undid that. So we're going to go back and forth, back and forth. And over the course of time, things will get worse and worse and worse. And the problem is that whenever we think we've hit rock bottom, we go lower. Things get worse. Now we have a pandemic. So it's really frustrating. And I don't want to make this video to get everyone down and make them feel depressed. But we have to be realistic about what we're working with. We can't delude ourselves into thinking that Joe Biden is going to be good or even competent because I don't believe he will be good or competent if he beats Donald Trump. Well, okay, Trump's out of office. That's that's good. He's a psychopath. He's crazy. But at the end of the day, will Joe Biden actually change the country so we don't see another Donald Trump? No. Now, you know, some leftists may think, well, at least if Joe Biden loses, then, you know, we get to try again in four more years. But the problem with that is the damage that Trump causes in another four more years. I mean, it's it's going to be irreparable in some ways, right? Things that he does, we can undo them with a Democratic administration in the future. But a lot of what he does, you know, we can't, we can't undo that. Like when it comes to environmental degradation, we can't really undo that. We don't have another four more years to undo the progress that we've made when it comes to climate change. So it's not like things have to get worse before they get better. I genuinely don't agree that that is going to happen. Regardless of what happens, the outcome of this 2020 election, we're going to be in a bad place. And, you know, if you think that the left is going to have a better chance in 2024, the problem is that we have no leadership now. Bernie's not going to run again. So who's going to step up? Who's going to be that next left-leaning leader? What's probably going to happen is, you know, there's going to be that void that will need to be filled, but it's going to be filled by a corporate Democrat. There's going to be this vacuum left open, this space for left-wing politics in the Democratic Party. And we're going to see a charlatan like Obama come along and capitalize on it, but actually be a corporatist and not actually do anything to facilitate real change. And the reason why we could trust Bernie Sanders and that he would actually fight and not be a charlatan was because he has this 40-year track record. So the future, it looks grim. It looks bleak. But I think it's important that we're honest and open about this fact because if we lie to ourselves, then we're not really going to know what we're working with. If we misdiagnose the problems that we're dealing with, we're not going to be able to apply adequate solutions, right? If we delude ourselves into thinking we can tweet at Joe Biden to get him to adopt Medicare for All, we're never going to get Medicare for All. So the reason why I say this is to want to educate liberals who think that the left is just being babies and we're just butthurt because our guy lost. Now, this wasn't about Bernie Sanders. Bernie Sanders was a vessel for our ideas. That's all he was. That's it. So sure, we're mad that he didn't win, but this isn't just about our team losing. This goes deeper than that. This is about our future. And a lot of us don't feel like we have that. So that's part of the reason we need to educate people about where we're coming from. And I don't speak for everyone, but I mean, I can only speak for myself, but this is what a lot of leftists believe that the situation sucks either way. And another reason why I'm making this video is because if we know what we're working with, if we actually are realistic and we assess the situation, clear-eyed, not with rose-colored glasses about what could be and we know what we're getting, then we can, I think, be more effective in organizing. The best thing we can get out of a Biden administration that will last for a while is an RGB replacement. He gets to fill that seat if it becomes vacant. But aside from that, you know, we're not going to be able to convince him to adopt progressive policies. So within this time, we have to be real and think deeply about what we need to do as a collective to build power.  I'm talking about actually building power and not squandering what little leverage we have. So this is kind of an open-ended discussion. I can't, you know, concisely tell you what we need to do because I genuinely don't know. And this is a time where we should all be introspective. But what I am saying is that, one, we have to be realistic about what we're working with in a Joe Biden administration or a Trump administration. But either way, we're going to have to fight and we've got our work cut out for us. But what's most important about all of this is not that you take all of this as, you know, permission to give up. Because, oh, well, Mike says everything is bleak. Let's just check out a politics. No, not at all. That's not what I want you to take away from this. I want you to take away from this that the future has not yet to be written. It's not here yet, right? So we're currently headed down this really dangerous path. The trajectory that we're on looks bad. But guess what? We still, believe it or not, have time to change that. And it doesn't matter if Donald Trump or Joe Biden becomes president. Our actions shouldn't change, right? I mean, I'm not saying it doesn't matter like they're the same. Again, don't want to perpetuate a false equivalency. But what I'm saying is it doesn't matter insofar as the left, you know, decides what action we need to take because irrespective of what happens, whatever the outcome may be of 2020, we have to be united as lefties. And we have to be really organized. And I think more savvy going forward to actually become powerful and get the policies that we want implemented into law. Now, however we do that, I think we've got to think this through. But don't get down, get organized and really fight. That's what's really important. So, you know, I honestly don't know why I made this video. I wanted to kind of like give people who are libs this perspective, because I'm seeing people on, at least in my social circles, you know, on my Facebook timeline saying, oh, these Bernie bros, they're so insufferable.  But it's that's such an oversimplification and it's gross, right? Because that's not what this is about. That's, I don't care, right? I'm not loyal to any one politician or party. I'll switch allegiance, you know, like that if I can get the policies that I want codified into law. And if, you know, we get in this situation, that's not possible.  I'll switch allegiance. I don't care. This isn't about Joe Biden versus Bernie Sanders. I just want policies implemented into law that will help people. That's all I want. That's all I'm looking for. I'm easy to please, I think, right? Because it's not about party. It's not about politicians. It's about policies.  So I thought maybe this can be helpful for people who don't have that perspective, who don't know what millennials are dealing with. And also I thought, you know, it would be important for the left to really acknowledge what we're going to be working with because I don't want you to think that if Joe Biden is elected, everything is going to be peachy keen. But I also don't want you to think that, you know, if Donald Trump is reelected, oh, we're just going to try again and we'll definitely win in four years. You know, things don't often go according to plan. You know, my plan was for Bernie to get elected. Second time we're stronger. We know more. We can use what we learned from 2016 to get them elected in 2020. People change. Things change. And you know, a lot of things will be different in 2024. So don't bank on that. Don't only bank on electoral politics. But what I do know is going forward, try to be more savvy and try to realistically look at the situation that we're in so you know how to respond appropriately. And that's really all that I can say.


The chair knows the time is 6pm. I call this meeting of the Amherst zoning board of appeals to order. My name is Steve Judge. As ZBA chair, I want to welcome everyone to this meeting. We'll begin with the roll call of the ZBA members. Steve Judge is present. Ms. Hilda Greenbaum. Here. Mr. David Sloveter. Present. A quorum is present. Also attending the public hearing tonight is Ms. Christine Brestra, planning director, and Ms. Janet Mullins, who is our technical advisor for tonight from the town. Pursuant to chapter 20 of the Acts of 2021, extended by chapter two of the Acts of 2023, this meeting will be conducted via remote means. Members of the public who wish to observe the meeting may do so via Zoom or by telephone. No in-person attendance of members of the public will be permitted, but every effort will be made to ensure that the public can adequately access the proceedings in real time via technological means. The zoning board of appeals is a quasi-judicial body that operates under the authority of chapter 40A of the general laws of the Commonwealth for the purpose of promoting the health, safety, convenience, and general welfare with the inhabitants of the town of Amherst. In accordance with the provisions of Massachusetts general laws chapter 40A and article 10, special permit granting authority of the Amherst zoning bylaw, this public meeting has been duly advertised and notice thereof has been posted in mails to parties at interest. All hearings and meetings are open to the public and are recorded by town staff. It may be viewed via the town of Amherst, YouTube channel, and ZBA webpage. The procedure is as follows. The petitioner presents the application to the board during the hearing after which the board will ask questions for clarification or additional information. After the board has completed its questions, the board will seek public input. The public speaks with permission of the chair. If a member of the public wishes to speak, they should so indicate by using the raised hand function on their screen or by pressing star nine on their phone. The chair with the assistance of the staff will call upon people wishing to speak. When you are recognized, provide your name and address to the board for the record. All questions and comments must be addressed to the board. The board will normally hold public hearings where the information about the project and input from the public is gathered, followed by public meetings for each. The public meeting portion is when the board deliberates and is generally not an opportunity for public comment. If the board feels it has enough information and time, it will decide upon the applications tonight. Each petition heard by the board is distinct and evaluated on its own merits and the board is not ruled by precedent. Statutorily for a special permit, the board has 90 days from the close of the hearing to follow the decision. For a variance, the board has 100 days from the date of filing the final decision. No decision is final until the written decision is signed by the sitting board members and is filed in the town clerk's office. Once the decision is filed with the town clerk, there's a 20-day appeal period for an agreed party to contest the decision with the relevant judicial body and superior court. After the appeal period, the permit must be recorded at the registry and deeds to take effect. Tonight's agenda, public hearing on ZBA FY2024-08, WD Cowles, Inc. Request for modification to an existing comprehensive permit, ZBA FY2017-07, under Massachusetts General Laws, Chapter 48 and Sections 3.355.0 of the Zoning By-law to change the use of a commercial space from retail to a photography studio and to modify condition 88 at 81 Cowles Road, Map 5A, Parcel 139, COM Commercial Zoning District. There'll be public meeting on that same topic and a general public comment period as well as any new business. So the first order of business tonight is ZBA FY2024-08, WD Cowles, Inc. requesting a modification to an existing comprehensive permit, ZBA FY2017-07, under Massachusetts General Laws, Chapter 48 and Section 3.355.0 of the Zoning By-law to change the use of a commercial space from retail to photography studio and to modify condition 88 at 81 Cowles Road, Map 5A, Parcel 139, COM Commercial Zoning District. Are there any disclosures from members of the board? If not, we did not conduct a site visit at the site. We do have submissions and those can be found in the Project Application Report. Those include applicant submissions, FY2024 application form and FY2024 management plan, a cover letter by Arthur Haskins, dated 11, 1723, beside rendering by Coon Rital Associates, dated 11, 7, 2023 and floor plans, retail space portioned by Alain D. Tierney, dated 3, 29, 2022. We also have a staff decision document, which I think is the Project Application Report or is that a separate document, Christine? The staff submission is the decision that was originally prepared for this project in 2017. Oh, okay. The earlier, yeah, the first comprehensive permit, got it. Okay, we didn't get that. And I don't think this is... Yes, there is also the staff submission of the Project Application Report and I think that's on the top of the second page of the Project Application Report. Yep. The background, yes. In other words, there are two submissions, yeah. Yep, okay. Good enough. There's no public comment, right? No. I've been submitted. All right. So we should bring the applicant on as a participant at this point. Mr. Haskins, welcome. Thank you. Can you give your name and address for the record, please? Yes, my name is Arthur Haskins. My work address, I'm at W.D. Coles, 134 Montague Road in Amherst. Thank you for your time this evening. Great. Make a presentation. Yes. So I do have, in lieu of a site visit, queued up the ability to share some photos of the frontage that correspond with the drawings submitted with the application. Just a quick background, I'm the vice president of real estate and development at W.D. Coles. We are currently looking to get a new tenant into and up and running at the former location of the North Amherst library temporary location at 81 Coles. I submitted in our application a management plan describing her use as a photographer's studio. I should clarify, this is digital photography. There's no processing of any chemicals or films or traditional photography means this is purely an area that's to receive the public and staged for the actual photo shoots. And I have some interior pictures of the way that is staged today, ready for operation as well to help clarify. In addition to the use, I have also the, as you had noted, the Coon Riddle depiction of the front elevation revised to show soulful pet studios as the depiction of the name on the facade of the North Square commercial building A1 located at 75 Coles Road. If I may share my screen, I'll go ahead and walk you through just the elevation of the building, the location, and I think it may help with any questions and commentary that you may have as well. All right. Okay. Are you able to see my screen? No, we can, yes, the permit's done. Great. I'm gonna move this bar over. My apologies. This is the former approval for this space for the North Amherst Library. And that is the result. This was the most recent use. So this is the location, if you can see my cursor on the screen in pink, hovering over the North Amherst Library temporary sign banner. This is another angle depicting the address between the closet and here is another built business at 83. So this area right above the red van is the facade that is being depicted in the drawings for North Square. And I have one that I will share that may help understand the layout. This is the interior, the way she has it staged today. There's an area for reception for people coming in who are looking to have photos and portraits taken of babies and pets. And then there's some staging areas in the back for stations with props and things related to the photography business. In addition, I'll bring back up that front facade again, depicting soulful pet. I think that's actually all I have related to the use change and the signage. If I may pause there to offer time for any questions or requests. I have no question. It's the same style of sign all the way through all the, it's maintained the same all the way through the project, right? Absolutely, that's correct. We've been maintaining the same theme. We try to have all of our commercial tenants actually source the signs from the same set of vendors and within a spec so that they are consistent with North Squares, the theme that we have for the commercial signage. And so the space is accessible, correct? Right from the side wall? Yes. And accessible within? It is accessible within as well. And I should also clarify that no physical changes, no construction would be occurring whatsoever. There's no new interior walls, even our partitions. The only construction related activity would be hanging the new signage if it gets approved. Got it. Okay. Mr. Sloveter. So in hopes of torturing you as little as possible tonight, I've read everything in your application that seemed relevant. So my only question really is from what I've, other than the change of the sign, is there, if anyone looked at this building, would they have any idea that any changes were being made at all other than the sign? It seems to me that nothing is changing. You're correct, very correct, yes. Okay, thank you. I have no further questions. Ms. Greenbaum, do you have any questions? No, I just think that it's a little bit of micromanaging. One commercial business is the same as another, well, the other wasn't commercial, the other was the library, but they shouldn't need to be here, is my feeling. All right, do you have anything else you wish to present, Mr. Haskins? Only that this also is relevant to our request to remove that condition in the comprehensive permit related to the administrator review, fully agreed. We love the idea of being able to have a little bit more of a concise period of time from when our new tenant wants to move in, signs a lease, and then the approval process for the use and the signage. So if that would also be approved, I feel as though it would be great. I'm gonna ask Chris just briefly explain. I was trying to find how we are amending condition 88. And I noticed that in clause D, the applicant's letter removes the first sentence. That makes sense because it's already been built. So I suspect are we modifying 88 D by removing the first sentence? And then on E, it looks like we're removing the last sentence, but then condition 89 is identical to that, almost identical to the language that we're removing from E. Can you run, is that the change that the applicant is seeking, Ms. Brestra? I believe that in my understanding, the applicant is asking to remove condition 88 entirely and replace it with these two conditions that Rob Wachilla has outlined in his project application report. First of which is that all the conditions of the original permit remain in place except for condition 88. The second one is a rewording of condition 88 that allows administrative approval of uses that would normally require site plan review and the administrative approval is by the building commissioner. And that was something that was recently added to the zoning bylaw. And then I believe that the sub categories of A through E are essentially the same as they were originally. So it's really replacing condition eight with this condition two. And I've noticed that in Rob's right up here. Condition eight? Condition 88, I'm sorry. It's replacing condition 88 with condition two. Who? I noticed on the page of seven of the project application report that although he has three proposed conditions, the last one is numbered two and it should be numbered three. So that's my understanding that he's proposing three conditions, the second of which replaces the condition 88 in the original permit. And then, so the last thing is on page eight, this, it would be condition three, sub part D. Any changes to these approved documents? So it must just refer, it's just refers to the management plan, the facade rendering and the floor plans, not to anything else in the comprehensive permit. Right, yep. Those can be approved by the building commissioner if he deems that it's natural. Okay, all right.  Now I understand what you're asking. We'll get into the discussion about the motion we make in a second. I don't want to make, unless there's any other questions from board members, I just want to get the public a chance to comment before we move on. I don't think there's any public, is there any public comment, Jennifer? I don't see any. There's one attendee, but. No, there's one attendee, but no hand is raised. If the public were to speak, they should raise their hand or press star nine on their phone. Doesn't look like we have any. All right, if there's no further comment, is there any questions from the board before we move to public meeting? All right, what I would like to do is move to a public meeting while keeping the public hearing open in case we need to gather additional information. Public meeting is where we generally discuss this amongst board members and is not generally a opportunity for public comment. So it seems to me that you're right, Hilda and David, I'm not sure why, I know why they're in front of us, but I'm not sure that we really need to always have a ZBA meeting to change the tenant. If it's a change in the type of, so this would, the change here would result if I'm correct, Ms. Brestra, as long as the use is approved under the zoning bylaw for that area, they would be able to go, the owner would be able to approach the building commissioner to get approval for the new tenant without having to have a modification of a special permit or without going to the ZBA unless he determines that it's a substantial change. Is that correct? That's correct. That would apply to any use that's allowed by site plan review. Yeah. So that, so allowed by site plan review and that's pretty much the same as what's allowed in the, that is the same as what's allowed by the zoning bylaw. By the zoning bylaw for things that don't change the exterior of the building except for signs and lighting. And it looks like Ms. Greenbaum has a question. I just want to make sure that if at one point it tends to be a borrower and I club, it would automatically come back, right? It would because anything that requires a special permit needs to come back to you for a special permit. Okay. And so by doing this, for this project we reduce the number of times that they have to come before us for special permits to get a new tenant as long as that tenant is already, that use is already permitted under the zoning bylaw with by site plan review. Site plan review. That's right. All right. I have no further questions. Mr. Slovitar or Ms. Greenbaum, any further questions? No, can we combine it in the one motion? What does it mean? I'm going to try to get, well, we have to make, do we have to make any of these findings from the ZVA rules and breaks from section 4.5, Chris? I think it would be a good idea. Rob wrote them up in his project application report starting on page four. Four, yeah. And what I'm going to do is run through that we do, that section are the only findings that we have to make under this, that are applicable to this application. This section 4.5, which is, there is no limited impact. There's no environmental impact or limited environmental impact. Most of the other provisions are not applicable except for section 4.528, where it doesn't have any proposed adverse effects on municipal facilities. There's nothing until they're all not applicable until we get to the very end. If I'm correct, but here's 539 at master plan. That's, this is in performance with that. Go ahead. There's one that's 4.5213 about traffic congestion. He has a sentence written about that. So you might, you know, take that. Oh, I missed that. I'm sorry. Thank you. Staff has found the proposal and the board finds that the proposal does not substantially increase traffic. The tour guide studios are not high-lying businesses in the existing parking area transport can be used. Transportation can be utilized. 4.54, excuse me, that's not it. 4.56 deals with architecture features. 4.539 has a sentence. Partition conforms to the economic development aspect of master plan. I can finish that. That's correct. But 4.56 deals with architectural and it's only superficial changes, not substantially different from neighboring structures. And 4.5, 4.60 is again, increase in traffic. 4.61 deals with the non-residential use and structures. Permit has already been granted. The approval is new commercial and can be done with some majority. All right. There was another 4.59. Did you mention that one? Did I miss that one? Yes, I did. Thank you. All exposed areas will shall be screened from abutting properties. This deals with the visually blocking trash dumpsters. The applicant claims that trash areas are screened and not seen from the public right away. So I think that without objection, we have approved the findings and block. Quick vote on that. The chair votes aye. Mr. Slovitor. Aye. Screen bomb. Aye. And we have three conditions to approve this. Condition one, which is everything remains in place. Condition two is as described and discussed. And condition three is, as we discussed, that any substantial changes can be to this document before us tonight can be approved by the building commissioner if he deems them substantially come back to us in a public meeting. So the motion, are there any questions about the conditions? I think not. No. So the motion that we have before us that I would entertain is a motion to approve the modification of comprehensive permit ZBA FY 2017 dash 07 to allow for the change in the commercial tenant and to modify condition 88 with a language approved in this petition ZBA FY 20 24 dash 08 and to close the public hearing on this petition. Do I have such a motion? Yep. So moved. Do I have a second? Second. Is there any discussion on the motion? No. Ms. Brestrup, have we crossed all the T's and dotted all the I's? I think you have. Did your motion include approval of the conditions? Well, we didn't cross all the T's and dotted all the I's because I did not state that. That's right. That's why I'm so glad it was. I want to add that. Yes. And Mr. Sloverter, I'm sure you will amend your motion to approve all the conditions and make all those findings. Well, I will give that serious consideration. I have given it serious consideration and I modify my motion to include what you just said. Perfect. So the motion before us as modified is the vote tonight. If there's no further questions, we'll move to the vote. The chair votes aye. Mr. Sloverter? Aye. Ms. Greenbaum? Aye. Motion's approved. All right. Mr. Haskins, you have your change. And you have to come here less often. Mr. Sloverter? Did we also approve? I forget my motion already. Did we also approve the changes so that they do not have to come before us again? That was part of my well thought out and modified motion. Yes, yes. OK, good. And by your modification, especially of condition two, we did that. And that's why I put it in there. Yeah, that's exactly right. You thought that was good. Good. That's good. Yes, it's a well thought out motion. I thought so. All right. The next order of business is any public comment on any matter. It's not before the board tonight. So to the extent that anybody in the public will choose to speak on any matter except the matter before us tonight, then you do so. I don't see a hand raised or you're not getting a telephone call, so we're in good shape there. There's no further public comment. The next order of business is a new business and Ms. Breschle. Just what do we have for the schedule coming up? I know we have a January 4th meeting. Is that correct? The January 4th meeting is about the Ball Lane Amherst Community Homes project. And you'll be discussing waivers and conditions at that time. And Ms. Murray, Carol Murray has drafted conditions, which you'll be receiving tomorrow. OK. I have a question. Yes, Ms. Greenbaum. Are we going to have some more discussion about the local preferences before we start writing conditions? Yes, I think you will. It's a good idea to get the conditions drafted in a project like this and have at least two opportunities to discuss the conditions. And so one of the conditions is local preference. And then you will have a discussion about that when you get to that condition. That's my understanding of how Mr. Wachila has this organized. But it's in the past, when we've had comprehensive permits, we've found it helpful to have the conditions drafted. And the board can then review the conditions and also review findings. But it gives you an idea of all the different things that you have to discuss. So yes, you will have a discussion of local preference. Yeah. OK. And then do we have a meeting on January 11th? Is that correct? The meeting on January 11th is a continued public hearing from August on the Schutzberg Road solar project. I think that that will be a report by Tom Reedy, who is the attorney for the applicant about what has transpired in the interim. My understanding is that things have moved rather slowly. And so my assumption is that they will ask for another continuation. But there will be that public hearing on the 11th. And who is not going to be here on the 11th? I don't think Mr. Meadows is going to be. We'll have to go back through the panel. But I think I thought there were some. I know Miss, I don't know if Mr. Meadows is going to be in town in the beginning of January. So I think that's right. Yeah. So then you'll have to think about which date you want to continue the public hearing to. So you should all. Well, I don't think Mr. Sloveter is on that panel. I'm on the solar panel. We are. OK. So I have January 11th set aside. So I'm planning to attend that. So we have. You should think about what dates in the future you also have open so that Mr. Judge can help you to determine which date to continue the public hearing to. Yeah. So probably we'll have to go into February for that. So we'll look at February dates. And then I think the other person is Mr. Henry. He is. And I think Mr. White is also on that. So we'll figure that out. All right. That's I don't have anything else to discuss as we head out of the 2023 and into 2024. And anything from the board members, if not. No. All right. Well, I hope you all have a very happy new year. Thanks for again. Thanks for all your work this year. We did a lot. We got a lot coming up this in 2024. Thank you. Call out before the pistons lose number 29. Say it again. Mr. Brown. We got a whole hour before the pistons lose number 29. Wow.  If you were following the Detroit Pistons and their. No, no, I'm following the Celtics. Well, I think the Celtics are going to be the pistons tonight. I think so. It's going to be number 29 for the pistons. Breaks a record, I think, right? In a row. That's the step that I sort of like the pats on the socks. All right. Do I have a motion to adjourn? I'm moved. And seconded. Well, I seconded. I thought it was such a good motion. I second that motion. All right. We're setting a record time for being done with the meeting. It's 631. The vote occurs on the motion. Chair votes aye. Mr. Sloveter. Aye. Ms. Greenbaugh. Aye. Motion carries. We are adjourned. Thanks all. Have a happy new year to everyone. Everyone be safe. Thank you all. All right. Bye bye. Bye.