3. Consider a society in which each woman has a geometrically distributed number Z of female offspring, i.e., P(Z = j) = p(1 - p)', j = 0,1, 2. .., where pe (0, 1). Let X, denote the number of females in the n'th generation. Assume that Xo = 1. (a) Determine the probability of ultimate extinction of this process. The answer will depend on the magnitude of p. Consider all possibilities. (b) Determine E(X17). (c) Derive an expression for P(X2 = 0)