Q. 1. We have a number of independent events A,,i = 1,2,..., n, with P(A) = p for all i. Let X= IA, and Sn = Xi.

a. (1p) Express E[X] in terms of p.

b. (1p) Express E[S] in terms of p.

c. (1p) Compute the MGF of Xi.

d. (1p) Compute the MGF of Sn

e. (1p) Use the MGF of S,, to compute E[S]. (If you don't know the MGF of S, then just assume it is A/(-s) for some \ > s.)

Answer rating: 100% (QA)

a EX p b ES EX1 X2 Xn EX1 EX2 EXn p p p n times np c The MGF of Xi is given by MXit ... View the full answer