Suppose that two players A and B are trying to throw a basketball through a hoop. The probability that player A will succeed on any given throw is p, and he throws until he has succeeded r times. The probability that player B will succeed on any given throw is mp,
where m is a given integer (m = 2; 3; : : :) such that mp < 1; and he throws until he has succeeded mr times.
A) For which player is the expected number of throws smaller? (Hint: The total number of throws required by player A will be YA = XA+r, where XA is the number of failures obtained by player A before he obtains r successes. Similar argument applies to player B.)
B) For which player is the variance of the number of throws smaller?