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Poisson Random Variable

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Let X be a Poisson random variable with parameter 5, and let Y = min(X,5). (a) What is the p.m.f. of X? (b) What is the mean of X? (c) What is the variance of X? (d) What is the p.m.f. of Y (e) Compute E[Y}.

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The solution contains the determination of probability mass function, Mean and Variance of a transformed Poisson random variable.

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Since X follows a Poisson distribution with parameter 5, ...

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