stats and probability - bayesian estimator

extra notes for reference attached after question.

Problem: Binomial and beta Let X be binomial distribution with parameters m (given) and 6 (unknown), fats) = (m)6I(1 art-i\" a: = 0,1,...,m. :1? Suppose that prior is the beta. pdf with parameter a, ,6 (given), I'(a + [3) {11 _ ,81 I'(a)I'(;8)9 (1 6) 0