(Coupon collector’s problem). We are interested now in the time it takes to collect a set of N baseball cards. Let Tk be the number of cards we have to buy before we have k that are distinct. Clearly, T1 D 1. A little more thought reveals that if each time we get a card chosen at random from all N possibilities, then for k 1; TkC1 [1] Tk has a geometric distribution with success probability .N [1] k/=N. Use this to show that the mean time to collect a set of N baseball cards is N logN, while the variance is N2P 1 kD1 1=k2.