Bayesian Statistics Homework help

3. Suppose X; ~ binomial(n;, 0) for i = 1, ...,n and the prior for 0 is flat such that 0 ~ uniform (0, 1). Let X = (X1, ..., Xn) be a vector of random variables and x = (X1, . . ., d'n) a vector of observed values. (a) (3pts) Find the likelihood function. (b) (3pts) In this case, the posterior distribution is e|X ~ beta (a, b). Find a and b. (c) (3pts) Use properties of the Beta distribution to find E(0|X). (d) (2pts) Find the maximum likelihood estimator (mle) 0