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

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IID Given a random sample X₂ N(μ, o2) for i= 1,..., n, let X denote the sample average. Show that (X₁-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. IID Given a random sample X₂ N(μ, o2) for i= 1,..., n, let X denote the sample average. Show that (X₁-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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Since X1 and X2 are both random variables with a joint normal distribution the necessary and suffici... View the full answer