##### (Answered)-8.10 Establish that in the limit as k ? 8 , the pdf for the negative binomial NBi ( k, k/ ( k + ?...

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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.)

Solution ID:10137779 | Question answered on 16-Oct-2016

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