Question: Let X be a Poisson random variable with parameter . Show that P{X = i} increases monotonically and then decreases monotonically as i increases, reaching

Let X be a Poisson random variable with parameter λ. Show that P{X = i} increases monotonically and then decreases monotonically as i increases, reaching its maximum when i is the largest integer not exceeding λ.

Hint: Consider P{X = i}/P {X = i − 1}.

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