Exercise 2: (C.L.T.) Demonstrate the Central Limit Theorem for the Normal and Exponential Distributions.

• Sample k=1000 samples of size n=30 from the Normal(5,2).
• Compute the means for each of the k samples.
• Draw a histogram of these k sample means.
• Describe the shape of the histogram.
• Do the above steps again with the Exp(=1/3).

Exercise 3: Demonstrate the independence of the sample mean and variance when sampling from the Normal(5,2).

• Sample k=1000 samples of size n=30 from the Normal(5,2).
• Compute the sample means and standard deviations for each of the k samples.
• Plot the sample means versus the sample standard deviations.
• Compute the correlation between the sample means and standard deviations.
• Do the above steps again with the Exp(=1/3).