All code should be turned in when you submit your assignment. The code can only use numpy; you cannot use any other machine learning packages, like sklearn.

= Question 5. [25 MARKS] We have talked about the fact that the sample mean estimator X = 12-1 X; is an unbiased estimator of the mean y for identically distributed X1, X2, ..., Xn: E[X] = M. The straightforward variance estimator, on the other hand, is not an unbiased estimate of the true variance o2: for V = 121=1(X; - X)?, we get that E[V) = (1 - 1)o2. Instead, the following bias-corrected sample variance estimator is unbiased: 7 = mi 2-1(X; X)2. This unbiased estimator is typically what is called the sample variance. (a) (15 marks] Use the fact that E] = o to show that E[] = (1 - 1)02. Hint: The proof is short, it can be done in a few lines. (b) [10 MARKS] We also discussed the variance of the sample mean estimator, and concluded that Var[X] = 102, for iid variables with variance o2. We can similarly ask what the variance is