Let X1, ...Xn be independent random variables having the same distribution with a mean and variance 2. Let X = (X1 + +

Let X1, ...Xn be independent random variables having the same distribution with a mean μ and variance σ2. Let X = (X1 + ··· + Xn)/n. Show that E{

n i=1 (Xi − X)2} = (n − 1)σ2. [Hint: Since Xi − X = (Xi − μ) − (X − μ), we have n i=1 (Xi − X)2 = n i=1 (Xi − μ)2 − n(X − μ)2.]