3. Define Y as the number of failures one need to experience in order to observe the k- th success when conducting independent repeated Bernoulli trials. Then, the probability mass function of Y is the negative binomial distribution with parameter (u, k), that is [(y + k) k k f ( y ; k, " ) = [ ( k) I (y + 1) utk' k (1 )y, y = 0, 1, 2, ... where the probability of success p = k . For known k, show that this negative binomial uth distribution belongs to exponential family with form f(y;0) = a(0) b(y)exp(yQ(0) ) and find its natural parameter