Can you help me with the question below?

9 ~ Beta(a, )3), X1, . . . ,Xn | a '1'} Bernoulli(9). Recall that the posterior distribution is 6|X1,...,Xn~Beta(a+T,+nT) (a) What is the posterior mean of r9, i.e. its expected value under the posterior distribution, E09 | X1, . . . , X\")? (b) Find the posterior mode of 9, i.e. the value of 6 maximizing the posterior density. (Hint: it might be easier to maximize the log of the posterior density.) (c) Give a 95% credible interval for 9. Use the notation Fa, for the CDF of a Beta(o:j ,8) distribution. (d) Calculate P(Xn+1 : 1 |X1, . . . ,Xn)