1. The problem statement, all variables and given/known data Show that, quite generally, the Poisson Mass Function has the same value at λ (i.e. the average) and at (λ-1). 2. Relevant equations The Poisson Mass Function is p(x) = [e^(-λ) * λ^(x)]/(x!) 3. The attempt at a solution I started out by plugging in λ-1 into the equation to get p(x)= [e^(-λ-1) * (λ-1)^(x)]/(x!) but now I've gotten stuck. I'm not sure how to progress and prove this other than plug in different x and λ values. I've seen the graphs and such that indicate that λ and λ-1 share the same value, but I just can't figure out how to mathematically prove it.