Chapter 6, Problem 6.44P

The joint probability mass function of X and Y is given by $\begin{array}{l}P\left(1,1\right)=\frac{1}{8}p\left(1,2\right)=\frac{1}{4}\\ P\left(2,1\right)=\frac{1}{8}p\left(2,2\right)=\frac{1}{2}\end{array}$

a. Compute the conditional mass function of X given $Y=i,i=1,2$

b. Are X and Y independent?

c. Compute $P\left\{XY\le 3\right\},P\left\{X+Y>2\right\},P\left\{\frac{X}{Y}>1\right\}$.