13. Let Y have the negative binomial distribution with parameters k and and p, that is, Y is the number of failures observed in order to attain (a predetermined) k successes in a sequence of Bernoulli trials with probability of success p. Such a distribution is often considered when modeling count data where the variance is larger than the mean (an overdispersed Poisson). Show that the negative binomial family is an exponential family where the natural parameter is 0 = log(1 - p).

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