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Problem 3 (10 points). Assume that is a Poisson process with parameter A. 1. Find the conditional distribution of N° given Nt = n when S > t. Your result should be a well known distribution. Give the name of the distribution and state its parameter(s) 2. Suppose further that (N+)120 is the superposition of 3 Poisson processes (N¹ 1>>, with rates A1,A2,13. respectively, where A = Given that Nt = n find the conditional probability that = = = where k:1 + k2 + k3 = n.

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