Let X1, X2, X3 be conditionally independent given Z = z for all z with the conditional

Question:

Let X1, X2, X3 be conditionally independent given Z = z for all z with the conditional p.d.f. g(x|z) in Eq. (3.7.12). Also, let the marginal p.d.f. of Z be f0 in Eq. (3.7.11). Prove that the conditional p.d.f. of X3 given (X1, X2) = (x1, x2) is , where g0 is defined in Eq. (3.7.13). (You can prove this even if you cannot compute the integral in closed form.)