14.3 Show that if the probability of obtaining n events is given by the Poisson distribution with mean θ and the probability of θ is given by the gamma distribution with mean α/μ, and variance α/μ2, then the overall probability of obtaining n events is given by the negative binomial distribution as discussed in Sect. 14.3, and that the parameters of the negative binomial distribution are m = α, r = n + α, and p = μ/(μ + 1).