A07.3 Challenge Suppose X1, X2, . .. Xn are independent and identically distributed random variables, and let X be their sample mean. Define Y = Xi - X for i = 1, 2, ..., n. Show that X and Y: are uncorrelated for any i. Hint: by symmetry, if the result holds for Yl it will hold for any i. Write both X and Y1 as linear combinations, i.e. find constants {a;} and {b;}, j = 1, 2, ..., n, such that X = Ca;X; and Y1 = Cb;Xj. Use the vector results for covariances [3]