Have to find the posterior predictive distn:

3. [6pts] Let X, be the claim amount in year i. All X,JA = A for i 2 1 are iid and follow Exp(] ) with pdf fx.IA(x|A) = de-Mr, 1>0. The pdf of A is given by 2 Show that the predictive distribution fX.+.(X.....x. (xx1, ...,x,,) is a discrete mixture of two Pareto dis- tributions by identifying the mixing weights and the parameters of the two Pareto distributions