5.1 The negative binomial distribution gives the probability of having the mth success occur on the rth Bernoulli trial, where p is the probability of the occurrence of the success of a single trial. Show that the negative binomial distribution probability function is given by P(r, m) = (r − 1)! (m − 1)!(r − m)! pm(1 − p) r−m. (5.18) The mean of this distribution is m/p and the variance is m(1 − p)/p2. Hint: Consider the situation after trial r − 1.