2 Let X be a random variable with the Poisson distribution, parameter Show that, for w 1, 2, 3, , P(X w) P(Y ), where Y is a random variable having the gamma distribution with parameters w and 1

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Question: 2. Let X be a random variable with the Poisson distribution, parameter . Show that, for w = 1, 2, 3, . . . ,

2. Let X be a random variable with the Poisson distribution, parameter λ. Show that, for w = 1, 2, 3, . . . , P(X ≥ w) = P(Y ≤ λ), where Y is a random variable having the gamma distribution with parameters w and 1.

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