(a) For n = 100, p = 0.02, and r = 2, compute P(r) using the formula for the binomial distribution and your calculator:

P (r) = C_{n, r}p^r(1 – p)^n–­r

(b) For n = 100, p = 0.02, and r = 2, estimate P(r) using the Poisson approximation to the binomial.

(c) Compare the results of parts (a) and (b). Does it appear that the Poisson distribution with l = np provides a good approximation for P(r = 2)?

(d) Repeat parts (a) to (c) for r = 3.