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), py (y) and ps (s) denote the probability functions. If X I Y then MX+y (t) = Mx (t) My (t). Which of the following arguments is a valid proof? O Ms (t) = E(ets) = eE(tS) _ etX+ty O Ms (t) = E [ets] = E [extty] = E[etx ] . E[ety] O Ms (t) = E(ets) > E(1 + tS) = E(1 + tX + ty) > E(etx ) E(ety ) O Ms (t) = E(ets ) = >setsps (s) 2 1 + ), (ts) ps (s) = Ex ex px (x) . ), ety py (y) O none of these