Consider the situation described in Example 3.7.14. Suppose that X1 = 5 and X2 = 7 are observed.
a. Compute the conditional p.d.f. of X3 given (X1, X2) = (5, 7). (You may use the result stated in Exercise 12.)
b. Find the conditional probability that X3 > 3 given (X1, X2) = (5, 7) and compare it to the value of Pr(X3 > 3) found in Example 3.7.9. Can you suggest a reason why the conditional probability should be higher than the marginal probability?