Prove the Poi approximation of binomial probabilities.

7. Prove the Poi approximation of binomial probabilities. Claim: If X Bin(n,p) with np = (or p = A/ n) and large n, then px(i) i.e., approximated by a Poisson probability with rate A. x. Hint: Use (1 1; (1 A/ n) n + and (n i + 1)/ n + 1 as n + oc. The last assumption implies we use the approximation for moderate i only. Which of the following arguments justifies the Poisson approximation? All limits are as n + infty. -i) (a) (b) (c) (d) o e limnp = A, by assumption lim p) ( lim p) ( lim p) ( none of these -i) -i) n(n lim n(n lim