Let X Y denote a random vector and let X1 Y1 XN YN denote a

Let (X, Y) denote a random vector, and let ((X1, Y1), ..., (XN, YN)) denote a random sample of (X, Y) observations. Suppose that one wishes to estimate E(X) times E(Y), i.e., one wishes to estimate E(X)E(Y). Consider the estimator XY where X and Y are the sample means of X and Y respectively. Can you prove that XY is an unbiased estimator of E(X)E(Y)? Why or why not? Show that XY is a consistent estimator of E(X)E(Y).

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