I will continue with the central limit theorem and its applications. This example I have taken from Sheldon Ross's book on probability theory, see the idea here is that civil engineers believe that W the amount of weight in units of 1000 pounds that a certain span of a bridge can withstand without structural damage resulting is normally distributed with mean 400 and standard deviation 40. So, the weight which the bridge can withstand is random variable you know and so it is normally distributed with mean 400 and deviation 40. Suppose that the weight again in units of 1000 pounds of a car is a random variable with mean 3 and standard deviation 0.3. So, the different cars will have different weights. So, therefore, again we have treated this as a random I mean this example the weight of a car is treated as a random variable and therefore, the distribution and the distribution is normal approximately normal with mean 3 and standard deviation 0.3. How many cars would have to be on the bridge span for the probability of structural damage to exceed 0.1? So, at a particular time how many cars are there and then the weight of these cars exceeds the weight which can cause structural damage and so you want the probability of this whole random of this event to be more than 0.1. So, you want to estimate that you want to estimate the number of cars that would be on the bridge. So, that the structural damage can occur. So, we begin by defining p n as the probability that there are n cars on the bridge whose weight exceeds w because that is where. So, the event is this that when it exceeds w the structural damage can occur. So, therefore, this is same as p n. So, this is x 1 plus x 2 plus x n greater than or equal to w and that would be you can rewrite this as probability x 1 plus x 2 plus x n minus w greater than or equal to 0. Now, x i's where x i's is the weight of the i th car right x i denotes the weight of the i th car. So, this is the total weight of the n cars which are on the bridge at that time. So, and therefore, by central limit theorem because for n large we have said that when they are identically distributed random variables independent random variables because the weight of each car is independent of the other. So, then sigma x i sigma x j j varying from 1 to n would be approximately normal with mean 3 n and standard and variance 0.09 n standard deviation is 0.3. So, the variance of the weight of a car is 0.09 and therefore, the variance of the n cars is 0.09 right. So, this is approximately this. Now, w is independent of the x i's because the weight that the bridge can withstand is independent of the weights of the individual cars and therefore, when I write sigma x i minus w this is also approximately normal yes. And we will again revisit all these summation of random variables and their distributions, but right now we have enough machinery with us to say that sigma x i minus w because this is normal approximately normal this is normally distributed. So, sigma x i minus w is also approximately normally distributed and the expectation of the mean of this normal variate is 3 n minus 400 that is minus w. So, mean of sigma x i varying from 1 to n is 3 n and this is 400 and the variance of course, becomes with a plus sign comes with a plus sign. So, because they are independent. So, variance of this plus variance of w which is 1600. So, this is the variance and therefore, I can standardize. So, the whole idea is that this is my this is the variate I am looking at and I have said that this is standard this is normally distributed with mean 3 n minus 400 and variance this. So, when I standardize I will say this minus the mean divided by the standard deviation. So, that is standardize. So, now z is the standard normal variate and the event. So, when I standardize this probability now can be written as probability z greater than or equal to. So, on this side it will be minus of 3 n minus 400 I mean bracket minus 400 divided by the standard deviation. So, when I do this operation I mean this probability is the same as this probability because this I have standardize the normal variate to standard normal variate by dividing by subtracting the mean and dividing by the standard deviation. So, therefore, this is equal to this and so, z is approximately normal and now we want this probability to be greater than or equal to 0.1. And so, we look up the tables for the standard normal and we find that when z is greater than or equal to 1.28 this is approximately 0.1. So, from the normal tables I get that this number should be 1.28 for this to be equal to 0.1 and therefore, greater than or equal to you want see the whole idea is that if the number of cars n is such. So, now this number I can say that is equal to 1.28. So, therefore, if you take it equal to 1.28 then you get the you get an approximation for n and in the sense that if you write less than or equal to 1.28 then obviously, this probability will be larger and therefore, this will the whole thing will still be larger than 0.1 this is the whole idea. So, I get a value of n by equating this to 1.28 and then my n should be greater than or equal to 1.17. So, here of course, this is a little complex thing to solve, but you can do it or you can you know start by putting in values of n and then you can find out for which value of n this is you know almost equal to this or little less than this. So, one can the lot of numerical ways of actually getting the value of n which satisfies this inequality. So, we can do that and therefore, it turns out that n greater than or equal to 1.17 satisfies the above inequality and so that means, if there are more than 117 cars then the structural damage may occur with probability 0.1. So, there is a chance of 1 in 10 that the bridge will suffer structural damage. So, I this was another interesting example I I mean actually you can see the application in the sense that and then also I chose this example for the reason that this also is a random variable and therefore, to convert this event to this event and then to reduce this to stand to use the central limit theorem and transform this to a standard normal variate and therefore, get your estimate of the probability that structural damage will be caused to the it may the bridge may suffer structural damage. So, the interesting example the central limit theorem this is in a town of 20,000 people 44 percent support an upcoming referendum vote. You see say for example, the currently the hot thing is is is Anna Hazari going to form political party or not. So, you take a referendum that means, you might ask people to vote on this whether you should do it or not. So, let us say and it is the feeling is there. So, maybe this is a small town and the feeling is that 44 percent will only support the upcoming referendum, but so then what you do is you conduct a pre vote poll. So, this is happens very often media person do it lot of magazines they do it they conduct their own pre vote poll to get a feeling or the opinion and use of the eligible voters in the town and surveys 100 people. So, therefore, if you are conducting a pre vote poll of the eligible voters in the town and surveyed 100 people what is the probability that the that the survey will show that the referendum will pass. So, one needs to understand what we mean by the referendum will pass in order for a referendum to pass it requires a majority vote or 51 percent. See even though the feeling is there that 44 percent support, but you never know at the time of the voting more people may vote for the referendum and so on. So, therefore, when you conduct a pre vote poll and you want to and you have you surveyed let us say 100 people, then if in that pre vote poll it turns out that 51 percent or more support the referendum, then you can say that our pre vote poll suggest that the referendum will pass, but actually when the voting is done and then if more than 51 percent people who have voted people who have voted the 51 percent of those people if they have supported the referendum will pass. So, right now this is just conducting a pre vote survey of 100 people. So, then you want to know what is the probability that the referendum will pass. So, therefore, the question is and therefore, that means, out if you are taking a referendum if you are taking a survey of 100 people then you want 51 people to out of those 100 people 51 should say yes for the referendum or support the referendum this is what you want to do find out. So, the probability therefore, one can model the situation using binomial random variables. So, x i is I mean if the person supports if the voter or the people you are surveying they support the referendum then x i will be counted as a success otherwise it is a failure. So, you will say that sigma x i I varying from 1 to 100 is binomial 100 with mean as 0.44 into 100 because probability of success that means your p is 0.44. So, I am writing here I should have written only 0.44 this is not this is only here. So, the p is 0.44 and then the mean of the binomial distribution will be n p and you want to find out the probability that the people that you are surveying the 100 people that you have surveyed would they how many would support that means number of successes here should be greater than or equal to 51 because then the referendum will pass. So, and that is why I chose this because this is depicting a new situation and we are just trying to model it through this thing here and applying central limit theorem. So, this is the whole idea and therefore, so I hope this is clear that this is sigma x i I varying from 1 to 100 should be greater than or equal to 51. So, from this 100 people if they get a feeling that 51 or more will support the referendum then you know they can sort of advertise and they can try to influence people and say that our pre vote poll says that referendum will pass and so on. So, standardizing this where yet sigma x i I varying from 1 to 100 this will be sigma x i I varying from 100 minus 44 the mean of this random variable which is n p 44 divided by the variance which is n p q. So, 44 into 0.56 because your p is 0.44. So, q is 0.56. So, therefore, this is your variance and so under root of that the standard deviation. So, therefore, this probability is equal to this probability. So, this is greater than or equal to 51 minus 44 upon under root 44 into 0.56. Now, as I have been telling you that whenever you want to approximate a binomial probability by you know standardizing the random variable and using a standard normal probability then you should also use the continuity correction factor which I have not done here. So, anyway so therefore, so that would be if you are saying greater than 51 then it will be 50.5 that would be the right figure. But anyway, so you can do that computation later on. So, right now the whole idea is just to see that. So, therefore, so to get a feeling for the kind of numbers that you have that will the referendum pass or not. So, this is this and therefore, under root of this comes out to be 4.96. So, this probability and this is a standard normal variant. So, therefore, probability this is equal to or we are approximating this probability by probability z greater than or equal to 7 upon 4.96 which comes out to be 1.41. So, z greater than or equal to 1.41. So, this probability which from the tables gives you the number 0.079. So, therefore, this is a very small probability and hence the chance of the referendum passing is very slim. In the town is 20,000 and you are only surveying 100 people and when you know that the chances of you know there is a 44 percent support the upcoming referendum. So, the probability of you know 51 percent or more support the referendum is small and that is reflected here. So, through the central limit theorem you have made this approximation to the probability through the required probability and it turns out to be 0.079. So, the chances of when you survey the 100 people and ask for their opinion whether they support the referendum or not it shows that the chances are very small for the people. So, again when one can go on and on about the applications of central limit theorem and how to various different situations you can apply it. Then I want to get back to another thing where we had also sort of use we had used the central limit theorem, but probably did not and I had said that we will prove it later on. So, but I just want to add word of caution also to it. So, here this is that we had x equal to x is a binomial n comma p and then we said that if you want to compute this probability x less than or equal to s then you will have to compute these numbers and this can be quite messy right i varying from 0 to s n c i p raise to i 1 minus p raise to n minus 1. So, this can be quite cumbersome to compute, but then we said that we can approximate it by standardizing this thing and so here this is x minus n p divided by under root of n p q the standard deviation and then this is less than or equal to s minus n p. Now, you add 0.5 remember I had talked about the correction factor when you binomial is a discrete random variable and we are approximating it by a continuous distribution. So, therefore, this continuity correction factor is also added. So, you have 0.5 and this. So, therefore, this probability this cumbersome thing can be approximated by the normal probability which is s minus n p plus 0.5 upon under root n p q. So, and we look up the normal tables and we can compute this number. Now, the thing is that of course, when you are approximating the question does arise how good an approximation it is and see what happens is that when for a binomial distribution if your p is close to half then the binomial distribution is symmetric in the sense that the values keep on increasing and decreasing in a symmetric manner.  And so, but when your p is away from half then your binomial will be skewed may be to the right or to the left and in that case it is not necessary that your normal distribution will give you a good approximation of the binomial probabilities. Now, it is said often that if your n p is greater than or equal to 30 or n p into 1 minus p is greater than or equal to 10 then the central limit theorem will always give you a good approximation of the binomial probabilities, but these are empirical statements. In some cases it may turn out that when you have n p greater than or equal to 30 or n p into 1 minus p greater than or equal to 10 you may get good approximations, but it cannot be said that it will happen all the time because certainly symmetry plays a role. And for p small and n large such that n p equal to lambda is moderate. So, then in that case Poisson approximation may be a good approximation and I had when we were discussing discrete random variables I had shown you that how a Poisson probabilities can approximate your binomial probabilities, but then of course, the condition was that p small and n is large and n p is moderately small is reasonable number then Poisson may give a good approximation for the binomial probabilities. So, with this word of caution of course, we can these approximations can be used and they are very helpful. And so I just thought that once we have talked about the central limit theorem we have proved it and shown its applications. I will just revisit what we had done earlier when we talked about approximating the binomial probabilities by standardizing the normal variate and reducing it to a standard normal variate and then computing the problem. . Now, which has problems for you to try on Chebyshev's inequality central limit theorem and law of large numbers, weak law of large numbers. Now, the first problem is straight forward it says that a random sample of size n equal to 81 is taken from a distribution with mu equal to 128 and standard deviation sigma equal to 6.3. With what probability can we assert that the value we obtain for x bar will not fall between 126.6 and 129. Chebyshev's inequality. So, you can see that it will be you know the absolute value. So, x bar minus when you essentially are saying that would be greater than 129.4 and less than 126.6. So, I have given it specifically because I want you to then convert it to you in the form of when you are saying that it is when you apply Chebyshev's inequality or the central limit theorem. So, we have already tried given example I have discussed examples where you can compute both the you know you can compute the probabilities given that your n is 81 and the standard deviation and mean are given to you. Now, I just want to make a comment here is that you see it as we have seen through examples in the lectures that you know the number n. For example, the probability that you get the bound that you get by using Chebyshev's inequality on the probability on the required probability would be a loose bound and the central limit theorem will give you a tighter bound or tighter this thing on the probability. Now, the thing and of course, you can also say that, but one point that is important is that the probability when you computed by the central limit theorem may sometimes depend on the distribution that you have handling. Whereas, Chebyshev's is a universal inequality and therefore, it may give you a loose bound, but then it the number does not change with respect to different distributions. So, Chebyshev's is a general statement a universal statement and later on when I have occasion I will again point out the difference between the even though we say that Chebyshev's is a looser bound there are other advantages of using the Chebyshev's inequality. . Question 2 let the random variables y n have a distribution that is binomial n p prove that y n by n converges to p in probability. So, this is the use of your weak law of large numbers and I may have already done it for you in the lectures, but anyway go through it and try to prove it by yourself. Then the third problem is consider the sequence of x n consider the sequence x n of random variables where p n is x probability of x n equal to x is 1 if x is 4 plus 2 by n and 0 otherwise. So, now here you see the probability. So, x n is equal to x the probability of that is equal to 1 if x is 4 plus 2 by n does it converge in distribution to some random variable x. So, that means find out the you will define the cumulative distribution function as n goes to infinity can you find a distribution bridge. If so find the distribution function of x show that the sequence x n converges in probability to x also. So, it should be interesting thing, but we go by the basic definitions and then try to solve the problem 1 x 2 x n are identically independently distributed random variables with density function f x equal to 1 by theta and 0 otherwise it should be equal to this 0 less than theta less than infinity. Let m n be max of x 1 x 2 x n. So, m n is the random variable which is the maximum of these n sample values find the distribution function f n of m n does. So, does f n converge to some f yes it will see, but we will not talk much about it because the second part is a little difficult part, but you can certainly see that f n will converge to some f. So, find the distribution function f n of m n. So, that part is that you can do through the tools that you have already learnt right because when you find out the to find the distribution function you have to say probability m n less than or equal to t. Now, since m n is the max of x 1 x 2 x n this will reduce to a probability that each x 1 is less than t x 2 is less than t x n is less than t less than or equal to t. And since they are independent this will reduce to probability x 1 less than or equal to t raise to n. So, therefore you can sort of do it in the regular way and then see if you can get a feeling for convergence of f n that is all we will not talk in detail about it because this becomes a little complex. If you are given that f x is 1 upon x square and x varies from 1 to infinity 0 elsewhere. So, this is how you are defining this p d f and this is the p d f of a random variable x. Consider a random sample of size 72 from the distribution having this p d f right. So, that means the sample identically independently distributed random variables there are 72 of them compute approximately the probability that more than 50 of the items of the random sample are less than 3. See the thing is now that the problem I have included it is problem because there is 2 steps. See first is that you want that probability that more than 50 of the items of the random sample are less than 3. So, there is a probability I will use this here. See you are given that f x is 1 by x square 1 less than x less than infinity right. So, you are wanting to find probability x less than or equal to 3 this is the problem right that more than 50 of the items of a random sample are less than 3. So, this is x less than or equal to 3 this will be 1 to 3 of 1 by x square d x right. The probability that a random variable which has this p d f. So, then the probability of x less than or equal to 3 will be given by this which is minus 1 by x from 1 to 3 right. So, this is comes out to be minus 1 by 3 plus 1 which is 2 by 3. So, now what I will do is you are selecting a sample of size 72 and we will say that if a sample has a value less than 3 then that is a success. So, therefore, the probability of a success would be 2 by 3. So, now this gets converted to a binomial random binomial situation. So, where we are selecting a sample of size 72 and we say that if a sample value is less than 3 then it is a success. So, that means now the question is that with the from a binomial 72 comma p 2 by 3 I want a sample of the item. So, more than 50. So, that means you want that if you are writing sigma x i. So, random variable x coming from binomial 72 may be I can write it here. So, essentially what I am treating is that x is binomial 72 and this is this. So, I am wanting that probability x is greater than or equal to 50 and so when you standardize this will be x minus the mean is 2 by 3 into 72 which is this is 24. So, 48 and that will be 1 by 3. So, 9, 16, 4. So, this is greater than or equal to 50 minus 48 that is 4 this comes out to be 9 8 sigma. So, this is the whole thing. So, that is why I chose this example. So, therefore, you have converted this to binomial situation and then you are computing the approximate probability that more than 50. So, here again I am now using the central limit theorem I am standardizing the normal the variate there and then therefore, you are computing the approximate probability because to compute the actual probability would be you know you will have to sum up those 72, 50 and the binomial probabilities for 50, 51, 52 and 72. So, this is this problem now let us go to measurements are recorded to several decimal places each of these 48 numbers is rounded off to the nearest sum of these integers. So, when you say rounding off that means, if a sum of the original 48 numbers if the decimal is below 0.5 below 5 then you reduce you drop the decimal number point and if it is 0.6, 0.7 then you take it to the next integer. This is how we say that you when you round off the numbers right approximate by sum of these integers. If we assume that the errors made by rounding off are independent and have uniform minus 1 by 2 comma 1 by 2 distribution compute approximately the probability that the sum of the integers is within 2 units of the true sum. So, now here we are assuming that the errors made by the rounding off are independent surely that you can expect because the errors that occur are not dependent on each other. So, and then this. So, therefore, the rounding off that you are doing is between minus 0.5 and 0.5 as I said if the number is something like 10.4 then you will write it rounded off to 10 if the number is 9.7 you will round it off to 10 integer. So, therefore, you assuming that the error part that means, the actual number minus the rounding that difference is uniformly distributed between minus 1 by 2 and 1 by 2 right. The approximate probability that the sum of the integers is within 2 units of the true sum. So, therefore, what we are doing is. So, you have 48 errors 48 numbers that you are rounding off. So, your sigma and each is. So, yes I can again write here that your see epsilon i is the error in the ith number right. So, we are wanting that summation epsilon and each epsilon i is and this is a uniform minus 1 by 2 1 by 2 right. Each error is uniformly distributed. Now, you are wanting the probability that this thing should be less than or equal to 2. I think this is the question that the sum of the integers is within 2 units of the true sum. So, which means that total error that occurs should be within 2 of the original. So, that means sigma epsilon i varying from 1 to 48 this should be within minus 2 and 2 right. The error can occur either on the when you round down or you round up. So, therefore, this total error we are saying what is the probability that this error is within 2 of the original sum original sum of numbers. So, I have added up the errors and so this sum should be greater than or equal to minus 2 and less than or equal to 2. This is what we want to approximate this probability and that again by the use of central limit theorem we will say because now epsilon i's are all uniform. So, therefore, your sigma epsilon i expectation of this i varying from 1 to 48 is because the mean is 0. So, this is 0 they are all independent. The errors we have assumed are independent and similarly, the variance of sigma epsilon i varying from 1 to 48 will be some of the variances and which will come out to be. So, the variance here is remember it is b minus a whole square raise to b minus a whole square divided by a 12 b minus a whole square by 12. So, this is the variance here is 1 by 12 and so variance this will be 48 by 12. So, the variance will be 48 by 12 and therefore, standard deviation will be under root of 48 by 12. So, I standardize and here this is what we get and then you know by the normal this thing. So, it says that probability. So, this is actually equal to probability mod z is less than or equal to this is 48 by 12. So, this is 1 and that comes out to be 0.6826 from the normal tables.  So, therefore, that means the error can be kept within 2. The total errors of rounding up and rounding down can be kept within 2 with probability 0.6826. So, that is a very high probability, right. But if you look at a loose upper bound that means if you are suppose rounding up all the numbers then this will be 0.5 into 48 which will be 24. So, that means you know an upper bound on the number of total errors that can occur can be can go up to 24, right. But here this the central limit theorem gives you the idea that this the probability that the errors will be within 2 is reasonably high. So, this is something about the problem I wanted to talk to you about varying from 1 to and so on is a sequence of identically independently distributed random variables with expected value of psi n is mu and variance psi n is sigma square. Now, if S n is the sum of the first n sample values show that S n upon n goes to mu with probability p.  X n show that m g f of as n goes to infinity t greater than distribution of y n square see the notation because we could not get it. So, x n I am saying is chi square n. So, we have talked about the chi square n distribution also. So, here this is the notation it looks like in the print it looks like x n square, but it is actually chi square. So, x n is chi square n and then y n is x n upon n. So, because again we wrote x n instead of chi because chi was not coming out nicely. So, y n is x n upon n and show that moment generating function of y n will go to e raise to t as n goes to infinity for t greater than 0. So, it is defined for t greater than 0. So, this you can work out and then what is the limiting distribution of y n. So, once you get the limiting m g f of y n then you will be able to say what is the distribution of y n limiting distribution of y n this was the whole idea through this exercise. And then show that x n minus n where so x n is actually chi square n. So, chi square n has mean n and variance 2 n. So, therefore, now we are standardizing this. So, this is actually the use of you know central limit theorem because remember central limit theorem is convergence in law. So, x n minus n upon under root 2 n for n large will converge to a normal standard normal variate. So, this is again the central limit theorem. That x 1 x 2 x n are independent random variables with probability x i equal to 1 p and probability x i equal to 0 1 minus p for i varying from 1 to 2 n. That means each x i. So, x i's are identically independently distributed Bernoulli random variables p is of course between 0 and 1 and it is unknown. So, this is what we have to estimate I will get back to this thing. So, now if you define s n as x 1 plus x 2 plus x n and you fix your t. Then the problem says using Shebyshev's inequality how large an n will guarantee that the probability of s n upon n minus p is greater than or equal to t. So, the probability of this event is less than or equal to 0.01 no matter what value unknown p has. So, obviously we are trying to say that the we want to find out how many sample values we should take x 1 x 2 x n. So, that this ratio s n upon n or the average of the sample values is different from p by. So, greater than or t we have fixed. So, this difference greater than t probability of that is less than 0.01. So, you want to use Shebyshev's inequality. So, here by Shebyshev's inequality as we said this is s n by n minus p. So, this you want greater than t probability of this and this you want less than or equal to 0.01. Now, by Shebyshev's inequality because this is the variance of s n by n is because remember now your s n is what the each x i is Bernoulli. So, therefore, this is binomial and so this is the variance of s n is n p q and so 1 by n this would be n square. So, this is p q by n. So, therefore, by Shebyshev's inequality this probability is less than or equal to this is p q by n into t square and this you want to be less than or equal to 0.01. So, now what it says is p is unknown. So, q is also unknown and therefore, no matter what the value of p is now since maximum of p q we have already gone through this in the lecture also maximum p q is 1 by 4. So, if I take the if I write the maximum value here since n is in the denominator. So, this will I will get the value of n which is larger which is smaller. See what I am saying is that this probability is less than or equal to 1 by p q by this 1 by 4 into n t square and this we want less than or equal to 0.01. So, suppose I put this equal to 1 equal to 0.01 and this tells me that my n should be equal to from here n should be equal to if you take n to this side it will be 0.04 into t square and since I have written see. So, this value has come. So, 1 by 4 is the maximum value of p q. So, now that means for n greater than or equal to this this will always be satisfied less than or equal to 0.01. Can you see that? See here I am writing the maximum value this upon n t square is less than this. So, n would be greater than or equal to this. So, I am taking it. So, if I put the maximum value here then obviously, I get the value of n which will meet this inequality because n will be greater than or otherwise if I write the actual value of p q then what I get the value of n would be smaller than what I am getting here. So, therefore, you know this will always satisfy this inequality this is the idea. So, therefore, by Shebyshev's inequality this is the thing. Now, part 2 says that using C l t find the approximate n needed. So, that now here you see it has put the word minimum of this probability and the probability here that is the complement of the event that you had in the part a. So, therefore, it is the same thing because here the probability of less than t is greater than 0.99. So, exactly but the minimum part I will explain again here because this is now by central limit theorem by central limit theorem minimum this. So, minimum this probability will be attained when I put the maximum value of this. And therefore, the minimum when you write this here this will be twice phi and root n into t and this is 1 upon 4. So, 1 by 2 so that the 2 also comes here. So, this minus 1. So, that satisfies this and now you want to compute again this you want to say is equal to 0.99 which means that 2 of phi 2 root n into t is equal to 1.99 and now you can continue. And in fact, you will find out the value of t because I think may be you will complete the problem. So, this is 2 divided by this 0.99 and the corresponding z value here I think from the tables if you look up your it says that 2 root n t is 2.57. I mean I think that is a thing and so you can compute root n from here. And now what it says is again since you have the numbers I mean in this case your n square comes out to your n comes out to be equal to 2.57 divided by 2 into t whole square. And in the third part it asks you to when you fix the value of t I think the value of t is given 0.01. If you do this then it wants to wants you to compare. So, for example, from here when t is this for t equal to 0.01 n comes out to be equal to 250,000. And then when you compare it for the central limit thing I think this comes out to be well it is computed somewhere I have done it here. So, your n will be greater than or equal to 1650. So, this is the idea because the Shebyshev's inequality gives you a loose upper bound therefore, the numbers will be different. So, this is the idea behind this thing and now you can sit down and work it out yourself to get a better feeling is equal to 1.99 and now you can continue. And in fact, you will find out the value of t because I think maybe we will complete the problem. So, this is 2 divided by this 0.99 and the corresponding z value here I think from the tables if you look up your it says that 2 root n t is 2.57. I mean I think that is a thing and so you can compute root n from here. And now what it says is again since you have the numbers I mean in this case your n square comes out to your n comes out to be equal to 2.57 divided by 2 into t whole square. And in the third part it asks you to when you fix the value of t I think the value of t is given 0.01. If you do this then it wants to wants you to compare. So, for example, from here when t is this for t equal to 0.01 n comes out to be equal to 250,000. And then when you compare it for with the central limit thing I think this comes out to be well it is computed somewhere I have done it here 1 6. So, your n will be greater than or equal to 1 6 5 0 0. So, this is the idea because the Chebyshev's inequality gives you a loose upper bound therefore, the numbers will be different. So, this is the idea behind this thing and now you can sit down and work it out yourself to get a better feeling.


Hey guys, it's Nate, AKA The Foot Accountant. Welcome back to the channel. Today I'm talking about some potential investments that we can make as we get near the Ones to Watch promo that is gonna be starting this Friday, October 1st, inside of FIVA 22 Ultimate Team. Yes, Ones to Watch promo is coming. I know we've been worried about starting on Ultimate Teams and all this good stuff, but I wanna talk about what could be happening on the market with some cards that could get into the Ones to Watch promo. Now, of course, there's two different weeks. There's gonna be 26 players in total that are impacts for Ones to Watch, so I wanna talk about that. And also heading into today, on Wednesday, kind of just giving you a little market watch and taking a look at where the market is right now. We've seen the market continue to go higher on the meta aspect. A lot of players, new players going extinct today, Usman D'Abele, Campembe, there's a couple other cards. Venetius Jr. is about to go extinct almost, I think. So I'm talking some of these cards in the market rising up. Maybe it's time to cash out on a couple of these as we look towards a potential dip in the market heading towards Friday, where a lot of people will be scared with FIFA points being opened, with Ones to Watch's impacts. So I wanna talk about that and just kind of give a barometer of the market, of course, a little market watch as well. But first things first, we had new news yesterday on Tuesday from EA Sports. We have not one, not two, not even three, but four Ones to Watch cards from PSG. Now, the other three have been confirmed that already are going to be in FIFA and they confirmed today Sergio Ramos is the fourth Ones to Watch card that will be from PSG. Now in total, we have 10 Ones to Watch cards that are confirmed, Konate, Shaqiri's, SBC, Wijnaldum, Grealish, Alaba, Hakimi, Lukaku, Krisha Ronaldo, and Lionel Messi. Now, of course, you add Ramos to that and the Kama Vinga card that was confirmed, EA Sports tweeted out the Kama Vinga would be a card that would be involved with Ones to Watch. Now, also, this was tweeted yesterday. This is actually Fabrizio Romano. He has some ties with EA Sports and he released and he showed Kama Vinga, Andre Silva, and Saul. So technically we have 12 Ones to Watch cards. 12 of the 26 that we know of are already, I guess, released, you could say, or teased, Andre Silva and Saul going to be coming out as Ones to Watch cards alongside of all these other Ones and Ramos that we know about. So let's talk about the investment side. It's how can we make coins knowing that these cards are gonna have Ones to Watches? Well, of course, the thing is, when a card does get a Ones to Watch item, that means that their gold card goes out of packs. And you've already seen people speculating with this and already seeing people investing in some of these players that are confirmed for Ones to Watch. I think a lot of people are investing in Alaba. I think people are buying up Lukaku. And I even think from the news that we had today with Andre Silva and Saul, you're seeing some of their price graphs go up. Take a look at 82-rated Saul, which by the way, when I saw this guy's rating, when Chelsea released our ratings earlier on a couple weeks ago, I knew that he was getting a Ones to Watch because he had a pace upgrade and you know with all the other paced downgrades that happened to midfielders and attackers. When I saw an upgrade on this card, I said, man, EA is definitely upgrading the pace on Saul because they want to make his card look a bit more tasty for when they give it a Ones to Watch. And again, that was confirmed by Fabrizio today that he will get a Ones to Watch. But when that was confirmed, you see his price go from about 1.8K all the way up to 2.4 people went out and invested because they know that this Saul is going to be going out of packs. Now, is this a really good card to invest in? In my opinion, not really. I'm going to show you some cards from last year's Ones to Watch and show you how you can maybe think and potentially decide some players that you maybe want to buy as an investment as we get towards Friday. Now, the one thing to think about is again, there's going to be two teams. There's going to be two teams of Ones to Watch. So let's say these players that are shown right now like Wynaldum, Grealish, Alaba, Hakimi, not all of these cards are going to be in team one, right? There's going to be 11 cards in team one. They're going to do a mini release of three cards on Sunday. So there's going to be 14 cards until the next Friday. Then they'll do 11 plus three. And there will be a total of 28 players, actually. 28 players in Ones to Watch, I believe. So it's not confirmed that Ronaldo and Messi will both be in packs day one. They might do Ronaldo week one, Messi week two, or vice versa. There's a little bit of risk because you're not exactly sure when the card is going to go out of packs. But let me show you how this could work, right? Last year, Allen had a Ones to Watch card. And I believe it was not released before. Allen was a big transfer into the Prem. But it wasn't confirmed that he was getting a Ones to Watch. They drop his Ones to Watch card, and his gold card goes out of packs. Take a look at what happens. Allen's gold card goes out of packs on the Friday, October 9th. He goes from 79,000 coins. And into the next week, with all the people still building squads, still buying Premier League center defensive mids like this Allen, and still an in-demand card, he rises up to 101,000 coins. Now there's other sides to this, right? The reason why this gold Allen rose up is because he was not a confirmed Ones to Watch. A lot of these cards that are already confirmed, their golds, probably aren't going to rise up that much because people have already invested in them and have already bought them up, right? What you want to be looking for are cards that transfer this summer that potentially don't have a guaranteed Ones to Watch item coming for them. But that's where the reward is, right? Risk over reward. Now you think about some cards that you would expect to get a Ones to Watch, right? Definitely we're thinking of Sancho. Definitely thinking of Sancho as a card who would potentially get a Ones to Watch. Of course, a big transfer to Manchester United. We know that Ronaldo's getting a Ones to Watch. It just comes down to if another OTW card from Manchester United is going to get released, which I think there will. I think EA would choose Sancho over Veran. Now they could choose Veran. So Veran or Sancho, whichever one you technically want to quote unquote invest in, might be a decent buy. I think Sancho, in terms of an investment, would be a much better buy. He's only 30,000 coins compared to Veran being 300K. I know his card doesn't look that amazing, but this is a card that a lot of people on FIFA are excited to use this year because it has new links, right? He is in a new club, new links inside of FIFA for chemistry. He links to Ronaldo, to Bruno Fernandez, to Pogba, to all of those players that a lot of FIFA fans and GGMU fans like to use. That's why I like this Sancho card, right? And he still is really good dribbling. So even though he doesn't have an insane amount of pace, he's got five star skills and he does have 91 dribbling, which probably makes him feel really good in game. He also has that finesse shot trait, which is overpowered this year in FIFA so far. So I like this Sancho card as an investment. I really do. Let's talk about some other ones, right? Romero from Spurs. We don't have a ton of center backs except for Konate and Ramos confirmed yet. I think this could be a card that EA might sneak into once to watch as a pretty solid card already. It's an in-demand item. He's a lot cheaper as well. If he goes out of packs on Friday, this is like a top five or top, top five, I would say, Premier League center back in the game of FIFA right now. So I think if he would go out of packs, his gold card would definitely rise up as people use him in their squads, even though he's really cheap. That's a card I would keep a watch on. Subitzer from the Bundesliga, I think once to watch this year is gonna be dominated by the PSG cards we already have known, League One, PSG and the Prem. There's gonna be so many Prem cards in once to watch this year. I think that they're gonna be sprinkled in from some other cards from other leagues. I think Subitzer is one of those. He's got a pretty solid card. He's another cheap option that I would keep a look on. Aguero would be one that I would watch and also Antoine Griezmann. Antoine Griezmann with his transfer back to Atlético Madrid. I think is another card this year that could be getting a once to watch. I mean, if they're really, they're really starting to hype up this once to watch promo. And in some of their, like the early, the launch update pitch notes that EA released, they talked about once to watch and how it was a huge transfer window and they want to recognize that in FIFA by putting out some insane content. I think that Griezmann gets a once to watch this year. I think this is a really, really solid pickup even based off of the hype. Again, what you're really gonna see in when you make your coins, the profits are gonna come if the card that you invest in does actually get into once to watch. That's the risk in it, right? You're trying to find a card that you think is gonna get into once to watch. Now, a lot of these guys are gonna get in. Like last year, a lot of people were buying Alan because they thought he was gonna get in. But again, they picked a card that was meta, that was usable, that people would still be buying for their teams, even if he was out of packs. And I would agree that a card like Griezmann, a card like Subitzer, Romero, and Sancho would all fit that bill this year. So do a little bit more research. Find out some other cards that you think might get into once to watch. And that could be a potential investment for you.  And now, if it's a card that does not get in packs for a team of the week, for a once to watch team one, obviously there are two teams of ones to watch this year, just like there was last year. So keep an eye on some cards like, let's say Griezmann doesn't get into ones to watch team one, but there's still potential he could get in team two. So that could make for another investment opportunity as his card gets supplied and it drops down, but then it maybe goes out of packs the next week, right? So that would be something that I would keep an eye on as we had two ones to watch teams last year. That could be a situation that you see this year as well. So that is what I wanted to talk about first today. Is that potential of the ones to watch investment? Now, do some more research, find some other transfers, maybe like Victor Oseman, somebody who transferred, sorry, not Oseman, Oseman transferred last year. He had a ones to watch, but think about some other transfers to the Serie A maybe or to the Bundesliga or to the La Liga even, where EA is gonna have to put in some cards, just they can't just do Premier League and League One. So start to do your research again, remember some of the big transfers that happened this summer. EA likes to, again, choose a lot of high rated cards and a lot of low rated cards all in between to kind of make these ones to watch squad. So just kind of think through that stuff and who you think might be getting a ones to watch and then invest accordingly if you think that could be something that would happen. So that is definitely an investing method that you can do. Now, when would you buy these cards, right?  They're gonna start buying it. People have probably already been buying Sancho's as we've been loading up and as we've been gearing up towards ones to watch. But I think you would definitely have to get these buys in before Friday. Now, I know the market is kind of high right now. So maybe you find an opportunity where this card drops a little bit, maybe with some supply at division rivals rewards, which will come early Thursday or maybe even today with whatever content EA releases. Thursday as well, we have marquee matchups. I think as well as what I'm about to talk about with the market, I think that even on Thursday, as we head into Friday, people might start to sell some cards, like we saw last year, because people are afraid of the supply that's gonna be coming. So that might be a buy time for some of those items. So that is the ones to watch investment opportunity that I wanted to present you guys with today so that you can make some informed decisions on that. I might not be, but I might buy a couple of ones to watch cards so that it could go out of packs. We'll see. It's a little bit of a gamble. I might put some coins aside towards it, but we will see. Now let's talk about a few other things because today is Wednesday, right? And that means team of the week is going to be released. Now I wanna take a look at a team of the week prediction with you guys really quick. Now last week they released a team of the week early. Usually they released the team of the week at 6 p.m. UK, but last week they released it at 4 p.m. UK with the drop of EA access. Now I don't know when this team of the week two is gonna be released. It's either gonna be at 4 p.m. UK or 6 p.m. UK, so we're gonna have to keep a watch out for that. But I think this prediction from Foothead, sorry, looks really accurate. They've got Emile Smith-Rowe being the featured team of the week, item four's performance against Spurs. I think it's either Smith-Rowe or Saka gonna get hard from that game. But this team of the week, if this was the actual team of the week that gets released today, looks very, very usable. And I wanna talk about a few cards that are in here. Position Chains, Ascendio, and Kunku. Leipzig had a huge win over the weekend. Ones to Watch Hakimi. He is already confirmed to be having a Ones to Watch card. Some people think he's getting an inform this week for PSG's game over the weekend. I wonder if EA, if Hakimi gets an inform this week, and right now his gold card is extinct on the market, if Hakimi were to get an inform this week, that would make me wonder if he will not be a part of Ones to Watch team number one. That would make me think that if they're giving an inform, they want that inform to be out in packs, then they're gonna drop the Ones to Watch. But that's maybe me reading into it a little bit. I honestly do not know. If he's not in team of the week today, then that's potentially something where we would think, okay, maybe Hakimi is gonna be in Ones to Watch team one and not team two, based off him not being team of the week. So that's gonna be one of the interesting things that we do see today. If Taylor Hernandez gets an inform, that's gonna be a cracked out card. He's gonna be basically the best left back in the game. So that's gonna be something to watch out for. But the market in general, again, is what I wanna talk about, because we've seen a lot of prices continue to go up today. Since we didn't have content yesterday on Wednesday, you've continued to see a lot of prices go up and I just hit my first ever liquid, seeing it in the top left hand corner, one million coins, I think of 22, that is a dub. I started trading with some icons and I've been just trading with a lot of stuff. Last night, right after I recorded the video, I went out and I bought, I bought, what did I buy last night? I bought a Kessie, I bought a couple other cards that were just too cheap, right? You see that I've been trading with a lot of different items. I bought four Kessies and two Kempembe's last night. Now I sold the Kempembe's actually a little bit early, but as we've kind of seen as the trend, some of these cards, like as this video is being posted, some of these cards have actually dropped down a little bit, like Lukaku was 68K, now he's 65, Le Quat is 41, he had the same movement last night. He went to 46, back to 40, back to 45 today and it's now back at 41. Holland was over 105, he's now 97. So I'm just kind of keeping an eye on some of these cards this evening as we go from Wednesday night into Thursday, or sorry, Tuesday night into Wednesday to see if maybe we can get another possible investment look here with the same fluctuation that we had last night happening into today. So that's one thing I'm gonna keep a close eye on. Again, it's like a carbon copy. Now he's back to 43, but it's a carbon copy of what happened yesterday. So I'm gonna keep watching on this. And again, like I was mentioning, what the thing that I'm a little bit worried about right now as Theo Hernandez is actually extinct, and I think this has to do with him being potentially in team of the week today. Watch out for Theo Hernandez and the Hakimi cards. If they're not in team of the week, people might sell off their golds and you might see them on the market. That would be an interesting scenario to keep an eye out as well. But really watch out for the potential sell-off that could start today and into tomorrow on Thursday. This is kind of the first warning. I wanna talk about it. If you wanna sell some cards, we saw this happen last year inside of FIFA 21. You see the card, right? These cards, Kante was 386K on basically today. What would have been Wednesday? And that was a peak for him. He went down to 365 on the full game release and then went up after that, of course, for the Week in Leagues. And of course, as you know, a card that a lot of people got coins and upgraded to inside of their clubs. Take a look at a bombing. Last year went to 355 on basically today, Wednesday was a peak. He dropped off Thursday and Friday down to 316 and then rose up way after that, of course, after the full game release. So this drop-off right here, like we see on a bombing from last year, is kind of maybe what I'm expecting to see this year as well because we saw a drop-off heading into Saturday and Sunday as people were worried about card prices and the FIFA points that were coming out on Monday of this week. And then we saw the market really rise up nicely after Monday. I think the same thing's gonna happen again. So if you wanna take the coins on some cards, especially on the lower tier, especially on the lower tier, guys like Alan St. Maxman, we use this example all the time. I know this card is very overpowered in game, but this card is also 79 rated. Even Le Coix, who we're talking about as a very overpowered card in this game, I'm a little worried about it. I'm a little worried about this card because he is what, 77 rated or 78 rated? 79 rated for Le Coix. Same thing as St. Maxman. He's gonna get supplied a ton on Friday. He's gonna get packed a lot and his price is going to drop 100% guaranteed. Now it could bounce back, but this is the scenario where it gets interesting.  Or are you just gonna ride it out? Because as we saw with Abameyang and Conte, they both went higher from right now where they were on a Wednesday before the full game was released. They both went higher than that point later on, but they dipped and went down in the meantime. So that's kind of a decision that you might have to make and we're gonna talk about that a little bit more tomorrow. But I wanted to talk about the specificity of how I do think some people will start to take the coins and it might not be a terrible idea to take the coins on some cards that you have seen explode up in price in the past couple of days as we have seen the market rise exponentially with people getting on the game and stuff like that. So that is one thing that I would just be, I wanted to put that seed out there and start talking about it today. We're gonna talk about it more tomorrow, but if you did wanna take the coins on some cards, be my guest, be my guest. As a lot of these cards have risen up a ton even more. Again, you have more cards going extinct. Now we haven't had any price range updates today except for Benjamin Mendy's card. And we're gonna keep an eye on this because since we've had these cards go extinct, I would expect to see price ranges again. Probably happened Wednesday night tonight or into Thursday because I do believe I was looking back towards last year at the beginning of FIFA 21. And there were two price range updates that happened on the game before the full game release. So I would expect one more set of price range updates to happen on guys like Renato, Kempembe, Dembele, Hakini, Teo Hernandez, even guys like De Young, right? De Young was like 125,000 coins. He's 119 right now, but his max is 130. So there's a lot of cards that are getting very close to their max price range. Some cards, not a lot, but some cards are getting close to their max price range. And that's something to kind of keep an eye out for. So again, if you're trying to trade on this market and make coins like I am, position change and chemistry style trading and trading with icons is definitely a place to go, especially with SBC solutions. Everything that we talked about in the best trading methods video from just a couple of days ago is still working 100% on this game. And it's just there's so many ways to trade right now on the game that it is just fantastic and there's lots of ways to make coins, which makes it very fun. So that is kind of, I guess, a little bit of a market watch, market update for you guys and what is going on right now in this game. So that is the video for today, boys. If you did enjoy it, make sure to leave a thumbs up, comment down below if you have any questions and subscribe if you're new. It's been Nate the Foot Accountant. I will catch you guys later. Peace out.


Hello, this is Nick from Laptop Media, and today we will show you how to open the Intel version of the Lenovo ThinkPad L13 Yoga Gen 4. To get inside this device, you have to undo 8 captive Philips head screws, then pry the bottom panel with a thin plastic tool starting from the back. You can also remove the pen from its housing, but it's not necessary. You don't have to pry the front side. Tilt the panel until you hear a slight click sound, and then you can lift away the plate from the base. Please remember, it would be of great help to us if you just hit the like button and subscribe to our channel. That would motivate us to make even more and better videos for you. The battery in this device is a 46 watt hour model. To take it out, detach the connector from the motherboard, and undo the 4 Philips head screws that keep the unit fixed to the base. The capacity is enough for 14 hours and 17 minutes of web browsing or 10 hours of videos. To achieve that, you have to apply the balanced preset in the Windows power and battery menu and set the scheme for battery to balanced mode in the BIOS. The optional Lenovo pen is placed right below the battery. The WAN slot is for optional 4G connectivity. For storage, you get a single M.2 slot for 2242 Gen4 SSDs. The NVMe is covered by a metal shroud that has a thin thermal pad on the inside. We found another pad below the SSD. Sadly the memory is soldered. Still the maximum amount is 32GB of LPDDR5. 4T800MHz RAM in dual channel mode, which sounds plenty. The memory chips are rated at 6400MHz, but they work at 4800MHz due to platform limitation. The cooling is simple, a single fan, a heat sink, one heat pipe, and a heat spreader.


Hello, I am Dr. Mandy Swigert-Hobaugh from Georgia State University, or GSU for short, where I am head of the Library's Research Data Services Department. I'd like to introduce you to my department and specifically to our GSU Data Ready Microdential Badges Program, which we began last year in 2022. The Research Data Services Department, or RDS for short, was officially formed in 2016 and provides training and support in the following areas. Analytic tools and methods including R, SAS, SPSS, data, Python, and Envivo, quantitative qualitative and mixed methods, survey design, and machine learning. We also support data visualization tools including ArcGIS, Tableau, Social Explorer, and visualization using the mentioned software and coding languages. We support finding data and statistics primarily for social science, health, and business research purposes, and we support data cleaning and management. Our current RDS configuration is a mix of four dedicated RDS members, two affiliate subject librarians, and three graduate and two undergraduate assistants. We offer one-on-one help via consultations and custom sessions for courses and research teams. We also offer open workshops for all GSU students, faculty, and staff to attend, and since 2020, we have made recorded versions of our workshops available. And in January 2022, we implemented our GSU Data Ready Badges Microdentialing Program tied to our live and recorded workshops. We have two badge tracks. One is our Data Literacy Series Badges created to appeal particularly to our undergraduates. It teaches core data literacy skills and concepts with real-life examples using a variety of tools. We currently have the Data Ready Badge launched, but soon we'll have the Data Collection Badge and the Data Storage Telling Badge launched. Once someone earns these three badges, they receive the Data Literacy Series Badge. Our software and coding training badges are intended for anyone seeking to learn a variety of data analysis and visualization software tools and coding languages, including our Python, SPSS, SAS, Data, ArcGIS, Tableau, and Indevo. We have 10 badges launched, and we will launch our 11th badge soon. So how this works is those wishing to earn badges must first enroll in the associated track Course Via Stacks, which is the GSU-branded Canvas platform. These badges do not have course credit associated, so any GSU student as well as faculty and staff can enroll in the badge course for free to earn badges. Once enrolled in the track course, they select the badge module in Canvas for the badge they wish to earn. Pictured here is the InViva Ready Badge module. They then can either attend the live workshops or watch the recorded workshops. Our workshop series are typically five to seven and a half hours in total. They then take the module quizzes to demonstrate their learning of the workshop content. The quizzes typically include 10 to 15 multiple choice or true-false questions in total and are automatically scored by Canvas. Earners have unlimited attempts to score the 100% needed for each quiz. Once they score 100% on the final quiz of the module, congrats! They automatically earn the badge, which is distributed by Canvas in connection with the Badger platform. They then can share the badge via texting or emailing direct links or embedding code on websites or posting to social media, like this example of a GSU graduate student posting their InViva Ready badge to LinkedIn. Why should students and everyone get badges? Well, there are many reasons why students as well as faculty and staff should consider earning our GSU Data Ready badges. Our GSU Data Ready badges are a marker of achievement showing that badge earners took the initiative to learn data skills. An earned badge demonstrates actual learning rather than mere attendance at workshops since earners must complete quiz assessments to earn the badges. And finally, data skills are highly valued by today's employers across all industries. By getting GSU Data Ready badges, earners demonstrate the two current and potential employers that they are committed to growing the data skills that employers value. In the program's first year, there were a total of 345 badges earned. 54% were awarded to graduate students, 36% to undergraduates, and 10% to faculty and staff. There were 203 unique badge earners, each earning about two badges on average. And there was a near equal split of undergraduates and graduate students earning badges and student earners spanned 50 academic majors. So here is a breakdown of the 345 badges earned by badge and by status burner as an undergraduate, a graduate student, or a faculty or staff member. The Data Ready badge, which covers core data concepts and skills, was the most popular with 107 badges earned, followed by the Data Vis Ready badge, which covers Tableau and Social Explorer data visualization tools with 65 badges earned. Also, these badges were comparatively more popular among the undergraduate badge earners. The popularity of these badges compared to the other badges is most likely due to the content being more accessible to a wider audience and thus having a wider appeal. Because neither requires specialized or advanced level statistical or software encoding knowledge or skills. The remaining software encoding training badges were comparatively more popular among our graduate students, which came as no surprise given the associated workshops content lends itself to those with more specialized or advanced level data knowledge and skills. However, the comparative popularity of the R badges and the Python badge among graduate students over undergraduates indicates to our department a need to explore adding new R and Python training geared intentionally toward an undergraduate audience. As skills in these coding languages are highly marketable and thus vital for strengthening career readiness among undergraduates. Now, while the GSU Data Ready badges program is only one year old, we are aware of various GSU academic programs and professors who already have integrated badge earning into their curriculum, including the Master of International Business Program, the College of Law Legal Analytics certificate program, the Nursing PhD program, a credit bearing data jam course coordinated by the GSU Graduate School in which students can earn individual badges and also the course badge pictured here, the College to Career Initiatives Ready Set Go trainings, and various individual professors assigning badges in courses for either required or extra credit. And recently, I attended the GSU College of Arts and Sciences undergraduate and graduate council's meetings to promote the badges program as a low investment way to integrate data skills learning into course curriculum across all majors, including the humanities, which traditionally lacks data skills training. In conclusion, the success of our GSU Data Ready badges in its first year was encouraging, and we look forward to further developing the program. We've developed a model for other colleges and universities to follow, and I encourage those wishing to learn from our successes and challenges to contact me, Dr. Mandy Swiger, HOBA head of the Georgia State University Libraries Research Data Service Department at the email address shared here. Thanks so much. Bye-bye.


So, I was trying to come up with the best analogy for how economics is presented to the public, and I've narrowed it down to two. The Wizard of Oz and the Latin Bible. Bear with me. Whether or not you study or are even interested in economics, you will know one thing. It's complicated, and that's an understatement. But does it need to be as much as it is?  Using incredibly obscure jargon, mathematical equations, convoluted models, and a PhD to back it all up. But in the end, it turns out to be mostly a big contraption of smoke and mirrors, and the economists are revealed to actually be the man behind the curtain.  Or when the Catholic Church decreed that the Bible must only ever be written and spoken in Latin, and the educated kings had the time of their lives knowing that the uneducated and unwashed masses would have no way to tell if their translation of Scripture is true or total lies that the king recites to justify abuses of power. Such are mainstream economic doctrines. At its core, the economy is not the stock market, currency exchange rates, interest rates, booms and busts, or flashy charts that you see on Bloomberg and MSNBC. They are a part of it, but the economy is not the sum of these parts. The core of an economy is people and the choices they make. In fact, the definition of an economy is a system for the allocation of a society's scarce resources, not numbers moving up and down on a screen. One wise phrase that I got from one of my lecturers is that finance studies money, economics studies stuff. But economics is presented as finance to the public, like it's some sort of niche, scientific study of money and wealth. Economics is the study of people. We are people. The economy is us. Economics is a social science, not a hard science. Ludwig von Mises perfectly summed up why this is by saying that a human's actions are unique and non-repeatable. Whereas with a hard science like physics, you can use laboratory conditions to adequately measure environmental variables such as air temperature, pressure and object mass to calculate how quickly a hammer will hit the ground once it's dropped. What you absolutely cannot objectively measure is how humans will react to various changes, because humans are the most unpredictable things you could ever imagine trying to study. If there is one phrase that is used more than any other bio-economists, it is setteris paribus, which is Latin for all other things remain in constant. So it can be said, setteris paribus, a small amount of firms brings about higher prices. So you have two economic variables here, firms and prices, but explicitly ignore the immeasurable amount of factors that work in an economy in real time alongside them that can't be turned off and on by a switch like in a laboratory. My Latin Bible analogy works perfect here because those two words give economists a get out of jail free card to make absurdly sweeping claims and then base their actions off of them. And you might have heard the name Pareto before and likely him being given lots of praise. Vilfredo Pareto had a funny name but was originally an engineer who brought mass appeal for merging mathematical engineering concepts into the field of economics and as such he is the bane of my existence. Pareto tried to turn the social science into another kind of engineering and laid that foundation stone for Keynesian and neoclassical doctrine, which are the current mainstream, to base themselves off this false equivalency between social and hard sciences. Just as you would expect any mixing of two completely incompatible solutions, this mixture has been a disaster. Tipified by inflation, bubbles, tithany, and mass wealth redistribution from the poor to the rich.  Well, it is a self-protecting disaster as the ones who commit it shroud their actions through what is an impenetrable mystery of numbers, equations, and meaningless terms for the layman. The truth is that economics can be adequately explained and understood by barely using any of them. If you want to study economics, of course you'll need a high level of mathematical and analytical skills, but to understand what an economy is and what economic institutions like central banks do, you just need to be an adult with common sense and time to read about it. But like the Latin Bible, this new economic language is maintained to hide the doctrines that harm you so greatly. If the Keynesians of the world actually spoke English instead of using fraudulent terms to describe concepts that already have words, society would see them for the snake oil merchants that they truly are, peddlers of a dud product for their own enrichment and empowerment at your expense. These fake wizards use their fake knowledge of the arcane to just tell politicians what they want to hear. Do this and it will give you more power. One day I'll make a video decoding Keynesian terms back into real English so you can see that their fanciful theories make little actual sense and in fact sound terrible when they can't dress it up and rephrase words to hide their true connotations. And for neoclassical economists there is no more joy for them than sitting at a desk all day trying to think of what they call market failures so they can publish a book that other neoclassical economists will buy and then scurry off like rodents to tell their politicians, look master, another opportunity for conquest. This whole process is even more of a farce as neoclassicals base these so-called market failures against what they call perfect competition. Once again an economy is a group of humans and humans are not and never will be perfect. So they go about searching for imperfections all day long amongst a gathering of imperfect humans and when they inevitably find them they go to another group of imperfect humans and tell them to plug the hole. But of course the plug is imperfect so it ends up creating a much bigger problem than there was before. Let me give you an example with the most egregious of their market failures and the one which is their most popular, what they call imperfect information. Imperfect information is not a market failure it is literally a market feature otherwise called specialization. The so-called market failure of imperfect information says that the seller of a product normally knows more about the product than the buyer therefore the seller can rip them off and that's a failure of the market. The market feature of specialization says through practice an individual becomes more skilled in a given field than his peers and can perform it better. If your goal as a seller is to sell goods for a higher price and you can do it then congratulations you're well specialized as you should be. If you in fact mislead a customer or sold them a faulty product then you've committed fraud and just to remind the neoclassicals we knew what fraud was long before you put your massive brains together to come to our rescue but there is one school of economic thought that demystifies the artificial barriers to understanding what an economy is why it works and why it crashes. It doesn't rely on models to prove its validity it recognizes that economics is a social science first and that mathematics makes sense in analysis but not in explanation. It recognizes humans and their institutions for the imperfect beings that they are and says that they are overall far more rational than the elitists give them credit for and if they are left to work things out themselves they will not only find a way they will find the best possible way that is the Austrian school of economics. The Austrian school is demonized by the mainstream because it completely undermines the ivory towers that they enjoy it makes the understanding of economics accessible to everyone and it makes brilliant sense all the way through from start to finish whether you've never taken an interest in economics before in your life or you've been studying it for decades. It describes economics not as a category of engineering or mathematics but one of praxeology meaning the study of human action. All the factories in the world won't do anything unless humans act upon them humanity is responsible for all economic activity ever to happen without our actions there would be no production chalking all subjective human action up to concrete rules of behavior is so ridiculous that only the intellectual class would have the naivety to do it so remember the talking heads for the naive sicker fans that they are remember the economy doesn't start with thousands of charts but starts with us and our choices and remember that governments are not benevolent but are made up of humans just as flawed if not more than everybody else these are the very first keys to understanding what economics actually is how economies work and how they can be manipulated against you this video will serve as my preamble for a series I will start working on explaining the basics of the Austrian school of economics so use this mindset daily keep it in mind and take it easy