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1. Suppose that X is a nonnegative, integer-valued random variable, and let n and m be nonnegative integers. Show that gnX+m(t) = tm · gX (tn).

2. Suppose that the offspring distribution in a branching process is the Ge(p)- distribution, and let X(n) be the number of individuals in generation n, n = 0, 1, 2, . . . .

(a) What is the probability of extinction?

(b) Find the probability that the population is extinct in the second generation.

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