8.10 Establish that in the limit as k → ∞, the pdf for the negative binomial NBi(k, k/(k + λ)) random variable becomes the pdf for the Poisson P(λ) random variable. 8.11 Obtain the recursion formula f (x + 1) = ρ(λ, x)f (x) (8.98) for the Poisson pdf, showing an explicit expression for ρ(λ, x). Use this expression to conﬁrm that for all values of 0 < λ="">1, the Poisson pdf is always monotonically decreasing. Find the value x∗ for which the pdf attains a maximum for λ > 1. (See comments in Exercise 8.7.)
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