Hello. Could you please answer this Bayesian question?

Let X1,X2...Xn be random variables conditionally independent given p,

(|)=(|p)==1 where = (1,2,...n), with each Xi ~ Bernoulli(p). Suppose we assume that p~(,).

a) Derive likelihood function (|p) (2 marks)

b) Find the posterior distribution of p. (2 marks)

c) Show that the posterior mean can be written as a weighted average of the prior mean, and the maximum likelihood estimate of p, . (3 marks)