Consider the negative binomial distribution given in Definition 3.9. a Show that if y r

Chapter 3, Problem 3.98

(choose chapter or problem)

Consider the negative binomial distribution given in Definition 3.9. a Show that if y r + 1, p(y) p(y 1) = y 1 y r q. This establishes a recursive relationship between successive negative binomial probabilities, because p(y) = p(y 1) y 1 y r q. b Show that p(y) p(y 1) = y 1 y r q > 1 if y < r q 1 q . Similarly, p(y) p(y 1) < 1 if y > r q 1 q . c Apply the result in part (b) for t

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