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Statistics

1. Consider a branching process with reproduction mean m 1. Suppose also, as before, that X(0) = 1.

(a) What is the probability of extinction?

(b) Determine the expected value of the total progeny.

2. The following model can be used to describe the number of women (mothers and daughters) in a given area. The number of mothers is a random variable X ∈ Po(λ). Independently of the others, every mother gives birth to a Po(µ)-distributed number of daughters. Let Y be the total number of daughters and hence Z = X + Y be the total number of women in the area.

(a) Find the generating function of Z.

(b) Compute E Z and Var Z.

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Statistics and Probability, Statistics

Category:- Statistics and Probability
Reference No.:- M91695214

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