Let X and Y be jointly Gaussian random variables (which means that any linear combination of X and Y is Gaussian). If the covariance of X and Y is 0 , then X and Y are independent. Use this theorem to prove that: If X1,…,Xn denotes a random sample from N(?,?2), then for each i=1,…,n,X? and Xi?X? are independent. (Recall that if X1,…,Xn are independent Gaussian, then any linear combination of them is still Gaussian.)

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