Question: Let X be a Poisson r.v. with parameter , and p() = P(X is even). Prove that p() = 1/2 (1+ e ). Find

Let X be a Poisson r.v. with parameter λ, and p(λ) = P(X is even). Prove that p(λ) = 1/2 (1+ e−λ). Find the probability that X is odd.

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