3. (6 points) Every package of a chocolate includes a one of the c different types of coupons. Each package is equally likely to contain any given type of coupon. You buy one package each day with goal of mllecting all the c different types of coupons and winning an attractive prize announced by the chocolate mmpany. (a) Find the mean number of days which elapse between the acquisitions of the jth new type of coupon and the [j + ljth new coupon. Hint: (Let X j be random variable that represents the number of packages pur chased to get the (j + 1)th new coupon after obtaining the jth new coupon. X J- is one of the four random variables we studied in class. Identify the random variable and its parameter pf.) {b} Find the mean number of days which elapse before you have a full set of coupons. Hint: Write X = X; + X; + . . . + XC_1. Now, use the linearity property of expectation