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(1) Consider the following processes: There are No = 1 many individuals in the zeroth generation. The number of individuals N(2) Consider the processes from the previous problem modified so that the number of offspring which each individual has is Be

(1) Consider the following processes: There are No = 1 many individuals in the zeroth generation. The number of individuals N in the kth generation comes from each individual in the (k-1)th generation having Poisson(A) many offspring independent of all others. (a) Find a formula for E(Nk). (b) Suppose X1. Show that P(Nk 0) converges to unity as ko N. = 0) converg
(2) Consider the processes from the previous problem modified so that the number of offspring which each individual has is Bernoulli(p) distributed. (a) Use moment generating functions to determine the law of Nk for each k. b) Use the above to determine P(Nk0 (c) Give a simpler direct determination of P(Nk 0).
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spoission νκ folocos Poisson V k 2/ ד hus, (nr-iA -) Scanned with CamScanner

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