What are the parameters of the posterior distribution? 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) = 0e-by f(yla, B) = ga-le-By r(a ) Beta(a + 1, B + y) Gamma(a + 1, B + y) O Option 1 O Option 2 Beta( a, B + y) Gamma(a, B + y) O Option 3 O Option 4 Cannot be determined analytically