## Fishy Problem

#### Problem

Given $X$ follows a Poisson distribution, with mean $\lambda$, prove that $P(X = \lambda) = P(X = \lambda - 1)$ for all positive integer values of $\lambda$.

For example, if $X \sim Po(5)$ then $P(X = 5) = P(X = 4) = 0.175$ (3 s.f.).

Problem ID: 324 (30 May 2007)     Difficulty: 3 Star

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