I have a couple of questions that I am having trouble with. Both require finding a posterior distribution.
a) Consider a random variable X with pdf f_X(x|theta) = (3*theta)*(x^2) *(exp(-theta*(x^3)), 0 < x < infinity. Assume theta has a prior distribution which is gamma with alpha = beta = 4. Find the posterior dist'n for theta.
b) A pattern is assumed to follow a geometric dist'n, p_X(k|theta) =
((1 - theta)^(k-1))*theta, k = 0, 1, 2, ..., n. Assume theta has a prior dist'n that is uniform on [0, 1]. Find the posterior dist'n for theta.
Thanks for any help!