Problem 21 Given n i.i.d. random variables X1,X2,...,Xn, each with mean ,a and variance 02 > 0 (both unknown parameters), we saw in class that the sample mean Y = i211 X; is an unbiased estimator of the mean a, Whereas the socalled sample variance (X:- J)? 1 52: 1 n 121,: 1 is an unbiased estimator of the variance 0?. In other words, E(s2) = 0'2. Is 5 = V32 an unbiased estimator of the standard deviation 0? If not, does 5 tend to underestimate or overestimate the standard deviation? Hint: Very little computation is needed. Start by writing the formula for computing the variance of 5