This question is intended to show how the means of a large number of samples are related to the CLT. (a) Generate a large number of samples uniformly distributed in the range [0,100]. We will call this our total population. In MATLAB this can easily be done with: pop = rand([N,1])*100; Plot a histogram from the population. Does it resemble a uniform distribution? (b) Estimate the mean and standard deviation of the population. Compare this with the theoretical values for the mean and standard deviation from a uniform distribution in the range [0,100]. What differences do you see? (c) Randomly sample 50 points from the total population. From this sample population estimate the mean and standard deviation. How does it compare with the total population? Are they similar? Justify your answer. Hint: You can easily sample from the population using: sample = randsample(pop,50) (d) We will now try to see the CLT numerically. To do so, repeat (c) 1000 times and save the sample means in a vector. This vector represents 1000 random samples of . Now estimate the mean and standard deviation of . Also, plot an histogram of . What do you see? What can you conclude about the CLT? Does it apply here?