Question: Let X b(n, p) and Y (????). If ???? = np, so that X and Y have the same mean, consider the sequence

Let X ∼ b(n, p) and Y ∼ (????). If ???? = np, so that X and Y have the same mean, consider the sequenceP(X = n) P(Y = n)' n = 0, 1, 2,...

Show that the sequence ????n is first increasing and then decreasing, attaining a maximum at the largest integer not exceeding ????.

P(X = n) P(Y = n)' n = 0, 1, 2,...

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