Question: 29. Let J be a Poisson random variable with parameter . Show that P[X = i) increases monotonically and then decreases monotonically as / increases,

29. Let J be a Poisson random variable with parameter ë. Show that P[X = i) increases monotonically and then decreases monotonically as

/ increases, reaching its maximum when / is the largest integer not exceeding ë.

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

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