Let X be a Poisson random variable with parameter . a. Show that by using the result

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Let X be a Poisson random variable with parameter λ.

a. Show that

by using the result of Theoretical Exercise 4.15 and the relationship between Poisson and binomial random variables.

b. Verify the formula in part (a) directly by making use of the expansion of e^-λ + e^λ.

A family has children with probability qpⁿ, n ≥ 1, where α ≤ (1 - p)/p.

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A First Course In Probability

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Authors: Sheldon Ross

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Question Posted: Sep 09, 2021 02:45 AM

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Let X be a Poisson random variable with parameter . a. Show that by using the result

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P{Xis even} s even} =1+e-21

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