32. Let X1, . . . , Xn+1 be a sample from a population with mean and variance 2. As noted in the text,

32. Let X1, . . . , Xn+1 be a sample from a population with mean μ and variance

σ2. As noted in the text, the natural predictor of Xn+1 based on the data values X1, . . . , Xn is ¯Xn =n i=1Xi/n. Determine the mean square error of this predictor. That is, find E[(Xn+1 − ¯Xn)2].