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 exactly i (of the m) genes of any generation are of type 1, then the next generation will have j type 1 (and m−j type 2) genes with probability

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?

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m m m m-j j=0,1,..., m