Let (X,Y) denote a random vector, and let (X1, Y), ., (Xn, Yn) denote an i.i.d....

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Let (X,Y) denote a random vector, and let (X1, Yı), ., (Xn, Yn) denote an i.i.d. sample of size n from (X,Y). Suppose Var[X] < o and Var[Y] < oo. Consider estimating E[X]E[Y] using the estimator X,Y. (a) Can you prove that X,Yn is an unbiased estimator of E[X]E[Y]? Why or why not? (b) Show that XnYn is a consistent estimator of E[X]E[Y]. Let (X,Y) denote a random vector, and let (X1, Yı), ., (Xn, Yn) denote an i.i.d. sample of size n from (X,Y). Suppose Var[X] < o and Var[Y] < oo. Consider estimating E[X]E[Y] using the estimator X,Y. (a) Can you prove that X,Yn is an unbiased estimator of E[X]E[Y]? Why or why not? (b) Show that XnYn is a consistent estimator of E[X]E[Y].