Recall the Coupon Collector’s Problem described in Exercise 106 of Chapter 2. Let X = the number of cereal boxes purchased in order to obtain all 10 coupons.

a. Use a simulation program to estimate E(X) and SD(X). Also compute the estimated standard error of your answer. 

b. Repeat (a) with 20 coupons required instead of 10. Does it appear to take roughly twice as long to collect 20 coupons as 10? More than twice as long? Less?

Data From Exercise 106

Use derivatives of the moment generating function to obtain the mean and variance for the Poisson distribution.

As discussed in Section 3.4, obtain the Poisson mean and variance from RX(t) = ln[M_X(t)]. In terms of effort, how does this method compare with the one in part (a)?