Let X be the number of Bernoulli trials until, and including, the first success. Then X has a geometric distribution with parameter, 0, where 0 is the probability of success on a particular trial. The probability mass/function for X is 0(1 – 0)x-1. In Bayesian inference, the conjugate family for the geometric distribution is the beta distribution. So the prior distribution for 0 is beta (a, b), i.e., g(0) « 4a-1(1 - 0)6-1 1. Derive an equation for each the parameters of the posterior distribution of 0, which is beta (d',6'). 2. Suppose the prior distribution is beta (2, 2) and X = 4. State the posterior distribution of O and calculate a 95% credible interval for 0.