What is the distribution of the posterior? Show detailed solution

The exponential distribution is a candidate distribution for a positive random variable y, and has one parameter 0. Determine the posterior distribution of 0, i.e, p(Oly), if a gamma prior distribution is combined with the exponential likelihood. Note that the probability density function of an exponential distribution and of a gamma distribution is respectively given by, f(y|0) = de-By Ba f(yla, B) = _ga-1e-By T(a) O Exponential distribution Gamma distribution O Beta distribution Cannot be determined analytically