Question: Show that the binomial (n, p) distribution approaches the Poisson (µ) distribution as n → ∞, and p → 0 with np = µ held fixed. Consider the negative binomial distribution with parameters r and p = 1 - q. Let r → ∞, and let p → 1 so that rq = µ is held fixed.
a) What does the mean become in the l limit?
b) What does the variance become in the limit?
c) Show the distribution approaches the Poisson (µ) distribution in the limit.