Let f(x|r, p) denote the p.f. of the negative binomial distribution with parameters r and p, and let f(x|λ) denote the p.f. of the Poisson distribution with mean λ, as defined by Eq. (5.4.2). Suppose r → ∞ and p →1 in such a way that the value of r(1− p) remains constant and is equal to λ throughout the process. Show that for each fixed nonnegative integer x,
f(x|r, p) → f(x|λ).