n = = 2. Consider the branching process {Xn, n = 0, 1, 2, 3, ...} where Xn is the population size at the nth generation.

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N 2 Consider The Branching Process Xn N 0 1 2 3 Where Xn Is The Population Size At The Nth Generation 1 (54.19 KiB) Viewed 132 times

n = = 2. Consider the branching process {Xn, n = 0, 1, 2, 3, ...} where Xn is the population size at the nth generation. Assume P(Xo = 1) = 1 and that the probability generating function of the common offspring distribution N is 1 A(z) = 2(3 + (3 + 4z + 3x2 + 2z3). (a) Find the value of c. (b) Find P(N = 0) and E(N). (c) Write down an equation satisfied by the extinction probability for this branching 9 process. (d) Hence, find the extinction probability q. (e) Now assume that the offspring distribution is truncated so that each individual has at most two offspring. That is, for n <2, the probability that an individual has n offspring is now P(N = n)/P(N < 2). Calculate the new mean number of offspring and hence state the new extinction probability (no further calculations should be required). =