44. Suppose that a population consists of a fixed number, say, m, of genes in any generation. Each gene is one of two possible genetic types. If any generation has exactly i (of its m) genes being type 1, then the next generation will have j type 1

(and m − j type 2) genes with probability



m j

 i m

jm − i m

m−j

, j = 0, 1,...,m Let Xn denote the number of type 1 genes in the nth generation, and assume that X0 = i.

(a) Find E[Xn].

(b) What is the probability that eventually all the genes will be type 1?