Prove the Poi approximation of binomial probabilities. Claim: If X is Bin(n, p) with np = 1 (or p = 1/n) and large n, then Px(i) is approximated by a Poisson probability with rate 1. Which of the following arguments justifies the Poisson approximation? All limits are as n approaches infinity.
1) lim np = 1, by assumption
2) lim (1 - 1/n)ⁱ + 1
3) lim (1 - 1/n)ⁿ(n-1).(n-i+1) X (1-1/n)ⁱ
4) lim i! (1-1/n)
5) none of these