Statistics

3. (3 pts) Find the MGF of Y ~ NBin(r, p). 4. (3 pts) Suppose there are n independent Gaussian r.v.s, X; ~N(uj, ? ) for j = 1, 2, ..., n, with possibly different means and variances (i.e., may not be identically distributed). For any constants a;'s, find the MGF of a linear function of these n independent Gaussian r.v.s, i.e., the MGF of Y = alX1 + a2X2+ . . . anXn (= Eh_a; X;). Hint: Since Mx(t) = E(etx ), it is the case that E(eatx ) = Mx(at), i.e., the MGF of X evaluated at at