2. The Central Limit Theorem (CLT) shows that for sufficiently large values of N, the sample...

 

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2. The Central Limit Theorem (CLT) shows that for sufficiently large values of N, the sample mean of N independent and identically distributed x-distributions x2(k) is approximately given by a Normal Distribution with mean E[x(k)] = k and variance Var(x (k)] = 2k. Follow these steps (the first three are exactly like in Q1): N (a) Create a 2-by-3 array of subplots. Fix k = 3 and instantiate an array N = [5, 10, 50] and a variable size 100,000. (b) Using a for loop, for each value n in N sample a size x n array of samples from the distribution x(k) (c) Compute the sample average along each row (i.e. you should get size sample averages), and plot their histogram in a subplot. (d) Over the histogram (i.e. in the same subplot), plot the approximate density of the distribution of sample averages which is given by the CLT as described above. (e) In a separate subplot, display the QQ plot of the sample means versus their approximate distribution 2. The Central Limit Theorem (CLT) shows that for sufficiently large values of N, the sample mean of N independent and identically distributed x-distributions x2(k) is approximately given by a Normal Distribution with mean E[x(k)] = k and variance Var(x (k)] = 2k. Follow these steps (the first three are exactly like in Q1): N (a) Create a 2-by-3 array of subplots. Fix k = 3 and instantiate an array N = [5, 10, 50] and a variable size 100,000. (b) Using a for loop, for each value n in N sample a size x n array of samples from the distribution x(k) (c) Compute the sample average along each row (i.e. you should get size sample averages), and plot their histogram in a subplot. (d) Over the histogram (i.e. in the same subplot), plot the approximate density of the distribution of sample averages which is given by the CLT as described above. (e) In a separate subplot, display the QQ plot of the sample means versus their approximate distribution