Exercise 2.8 The negative binomial distribution p(y | ,r) = y + r 1 r 1 r (1

Exercise 2.8 The negative binomial distribution p(y | θ ,r) =  y + r − 1 r − 1  θr (1 − θ )y , y = 0, 1,..., (0 <θ< 1) expresses the distribution of the number of failures until r successes have been observed. Show that a beta prior distribution combined with a negative binomial likelihood, results in a beta posterior distribution.