Let X be a random variable with the negative binomial distribution with parameters r and p.

(i) Let Y = X − r. Find the probability function, the expectation, and variance of Y.

(ii) Assume that, as r → ∞, the probability of a failure q = 1 − p converges to zero

(so that p → 1) in such a way that the product rq converges to a positive constant ????. Show that

Transcribed Image Text:

lim P(Y = y) = e- y!' y = 0, 1, 2, ...