Suppose that X Y is a random vector and assume that EYX the

Suppose that (X, Y) is a random vector, and assume that E(Y|X) = theta X. Let Z = Y/X. Is Z a random variable? Why? Show that E(Z) = theta. Let ((X_1, Y_1),...,(X_N, Y_N)) denote a random sample of (X, Y) observations. Let W = 1/N (Y_i/X_i). Using your result from above, show that: W is an unbiased estimator of theta. W is a consistent estimator of theta.

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