Chapter 4.1, Problem 3E

Let the joint pmf of X and Y be defined by $f\left(x,y\right)=\frac{x+y}{32},x=1,2,y=1,2,3,4.$

(a) Find $f_X\left(x\right)$, the marginal pmf of X.

(b) Find $f_Y\left(x\right)$, the marginal pmf of Y.

(c) Find $P\left(X>Y\right)$.

(d) Find $P\left(Y=2X\right)$.

(c) Find $P\left(X+Y=3\right)$.

(f) Find $P\left(X\le 3-Y\right)$.

(g) Are X and Y independent or dependent? Why or why not?

(h) Find the means and the variances of X and Y.