Homework 12: Jointly Distributed Discrete Random Variables

1. Section 3.2, #7, Section 3.3, #8.
2. Section 3.4, #2(a)(c)(d)(e), Section 3.5, #2(a).
3. Four cards are drawn from a deck. Let \(X\) be the number of kings drawn and \(Y\) the number of queens.
   1. Find \(f_{X,Y}(x,y)\).
   2. Use part (a) to find the probability that exactly 2 kings are drawn.
4. Two dice are tossed. Let \(X\) be the number of 2's that appear and \(Y\) the number of 3's. Write the matrix giving \(f_{X,Y}(x,y)\). Define a third random variable \(Z\) by \(Z=X+Y\). Use \(f_{X,Y}(x,y)\) to find \(f_Z(z)\).