Question: Let X be a Poisson random variable with parameter A. Show that PIX ) increases monotonically and then decreases monotonically as i increases, reaching its

Let X be a Poisson random variable with parameter A. Show that PIX ) increases monotonically and then decreases monotonically as i increases, reaching its maximum when i is the largest integer not exceeding 2.

Hint: Consider P(X = i\/P(X = i - 1].

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