Let X ∼ Poisson(λ).a. Show that if x is a

Let X ∼ Poisson(λ).
a. Show that if x is a positive integer, thenР (X — х) Р(X — х — 1) х b. Show that if X ∼ Poisson(λ), the most probable value for X is the greatest integer less than or equal to λ. Use part (a) to show that P(X = x) ≥ P(X = x −1) if and only if x ≤ λ.

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