Question: 4. In a branching process, an individual can have 0, 1, 2 and 3 descendants, each with equal prob- abilities. Start the process at generation

4. In a branching process, an individual can have 0, 1, 2 and 3 descendants, each with equal prob- abilities. Start the process at generation 0 with a single individual. (a) Compute expected population size at generation 5. [3 points] (b) Compute the probability that the branching process ever dies out. [3 points) (c) Compute the probability that the process dies out given that the population at generation 1 consists of 4 individuals. [3 points)

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