Let {Xk}, 1 k n, be a sequence of random variables, all with mean and variance 2,

Question:

Let {Xk}, 1 ≤ k ≤ n, be a sequence of random variables, all with mean μ and variance σ 2, and Yk = X*k be their standardized versions. Let Sn and Tn be the sum of the Xk and Yk, and Sn and Tn their standardized version. Show that S*n = T*n = Tn/√n.