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\f(3) Let the conditional probability density of X , given A to be Poisson in other words: BAAJ: = 0 1 2 A = z! 17 7 7 3 \"ml ) { 0 otherwise } Also, let A (the intensity rate of the Poisson distribution) to follow a Gamma distribu- tion with two parameters a and ,8. In other words, we have the following: (A) _ SELF15m (A and Cl! and ) >0 9 0 otherwise Prove that the conditional p.d.f. of f1()|:r) also follows a Gamma distribution. (20 points) Hint: The gamma integral I'(or)=f (swan-Ida o