Suppose a parent has no offspring with probability 1/2 and two offspring with probability 1/2. If a population of such individuals begins with a single parent and evolves as a branching process, determine: (A) the mean and variance of Xn. (B) un, i. e., the probability that the population is extinct by the n-th generation, for n = 1,2,3,4,5. (C) u[infinity] using the probability generating function of the offspring distribution, and illustrate graphically the result obtained.
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