Question: Prove Theorem 4.3. Let S X -+- Y, and let Mx(t), My(t) and Ms(t) denote the m.g.f. of X, Y, and S, respectively. Similarly,

Prove Theorem 4.3. Let S X -+- Y, and let Mx(t), My(t) and Ms(t) denote the m.g.f. of X, Y, and S, respectively. Similarly, let px(x), pv(y) and PS(s) denote the probability functions. If X Y then Mx+Y(t) Which of the following arguments is a valid proof? (a) (b) (c) (d) Ms(t) EUS) _ Ms(t) E[etSl E[efX+ty Ms(t) E(etS) + IS) + tx + tY) Ms(t) E(efS) etsps(s) 1 + none of these

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