Question: IID Given a random sample X N(, o2) for i= 1,..., n, let X denote the sample average. Show that (X-X2)X, i.e., they are

IID Given a random sample X N(, o2) for i= 1,..., n,

IID Given a random sample X N(, o2) for i= 1,..., n, let X denote the sample average. Show that (X-X2)X, i.e., they are independent, using the fact that, for random variables that have a joint normal distribution, the necessary and sufficient condition of independence is zero covariance.

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