Suppose a rv X has an exponential distribution with paramete

Suppose a r.v. X has an exponential distribution with parameter theta. That is, fx|theta(x|theta)=theta e^theta x for x>o, and 0 otherwise. Further, assume that theta has a gamma distribution with parameters alpha and beta. That is, f theta(theta)=beta^x^akoga-1e^-beta x/T(alpha) for x>0, and 0 otherwise. Find the distribution of f theta|z(theta|x). What is the name of this distribution with the new parameter9s)?

Solution