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PROBLEM # 4: Suppose we observe 3 sets of independent random variables: X1, X2, ,Xn w M63, (:2); Y1, Y2, ... ,Yn ~ may, 0'2]; and 21, Z2, ...,Z.n ~ mam + 91,, 02), which are also independent of each other. Let SE = Z?=1(Xif)2/(n1), 83 = Z?=I(K?)2/(nl),and SE = E?=1(Zi)2/(n1), where f, V and Z are respectively the sample means for the X's, Y's and Z's. Also we let 5'2 = (1/3)(S + 33 + SE). 4.3 Let _ _ _ X + Y Z T = . S One argues that a x T, where a is a constant, follows a t-distribution. If you agree with the statement, please provide the constant a and an appropriate degree of freedom, and justify this statement. Provide justication why this is incorrect if you don't agree with the statement