2.14. Five cards are drawn at random and without replacement from a bridge deck. Let the random variables \( X_{1}, X_{2} \), and \( X_{3} \) denote, respectively, the number of spades, the number of hearts, and the number of diamonds that appear among the five cards. (a) Determine the joint p.d.f. of \( X_{1}, X_{2} \), and \( X_{3} \). (b) Find the marginal probability density functions of \( X_{1}, X_{2} \), and \( X_{3} \). (c) What is the joint conditional p.d.f. of \( X_{2} \) and \( X_{3} \), given that \( X_{1}=3 \) ?