The hypergeometric distribution can be approximated by either the binomial or the Poisson distribution. (Of course, it can be approximated by other distributions, but in this exercise we will concentrate on only these two.) Let X have the hypergeometric distribution

(a) Show that as N → ∞, M/N → p,

(Stirling’s Formula from Exercise 1.23 may be helpful.)

(b) Use the fact that the binomial can be approximated by the Poisson to show that if N → ∞, M → ∞, K → ∞, M/N → 0, raid KM/N → λ, then

(c) Verify the approximation in part (b) directly, without using the Poisson approximation to the binomial. (Lemma 2.3.14 is helpful.)

N-M nx.ru , ar, K- . - , z=0, i, . . . .