Recall the coupon collector problem discussed in class which has many applications in computer science. Consider a bag that contains N different types of coupons (say coupons numbered 1 . . . N). There are infinite number of each type of coupon. Each time a coupon is drawn from the bag, it is independent of the previous selection and equally likely to be any of the N types. Since there is an infinite number of each type, one can view this as sampling with replacement. Let T correspond to the random variable that denotes the number of total coupons that needed to be collected in order to obtain a complete set of at least one of each type of coupon. Write a R simulation code to estimate E(T) considering the following: • N denotes the total number of coupons. Run your numerical simulation to develop an estimate of E(T) and plot E(T) for N = 10, 20,30,40,50,60. (Use 1000 trials or more, i. e, Nsim > 1000).
• We showed in class that for large N, E(T) can be approximated by N log(N) +0.577N +0.5. In the same plot show the theoretical value and summarize your observation regarding the accuracy of the approximation.