In Exercise 14 of Section 5.1 and in Exercise 12 of Section 5.4, you were asked to show that the probability function of both the binomial and the Poisson distribution satisfies the recursive formula

In the first case, the formula holds for x = 1, 2,…, n, in the latter for x = 1, 2,…, i.e. for all positive integers.
Show that this recursive relationship also holds for x = 1, 2,…, in the case of the negative binomial distribution and identify the choices of a and b for this case.

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f(x) = (a+b) f(x-1). (5.18)