Wanted to confirm if the answer I got, m^2 is correct for this text book problem.

Went per the hint. E[X] = Sum (E[Xi]) = m * E[Xi] = m * m , since E[X] for geometric variable is 1/p, and p here is 1/m.

42. Suppose that each coupon obtained is, independent of what has been previously obtained, equally likely to be any of m different types. Find the expected number of coupons one needs to obtain in order to have at least one of each type.| Hint: Let X be the number needed. It is useful to represent 31' by m x = 2X.- i=1 where each X,- is a geometric random variable