2. Despite its bias, the plug-in estimate of the variance actually has smaller Expected Squared Difference (ESD) from the target value, 2. Demonstrate this fact as follows:

A. Simulate 1,000,000 samples of n=5 observations per sample from the N(70,10) distribution. (The true variance, and therefore the target of the estimation, is 2=102=100.) Calculate the 1,000,000 estimates of 2 using the "n-1" formula. Using the Law of Large numbers, estimate the ESD of the unbiased estimates.

B. Repeat A. for the plug-in estimates (the "n" formula).

C. Which estimator tends to be closer to the target, the unbiased estimator, or the biased plug-in

estimator? Use your answers to A. and B. to answer this question.

D. Repeat A. and B. for the corresponding standard deviation estimators. Note: The true standard deviation, and therefore the target of the estimation, is =10).

E. Repeat C., but using the standard deviation estimators. Use your answer to D. to answer the

question, "Which estimator tends to be closer to the target of =10?"