1. (10 points) The joint probability mass function of $X$ and $Y$ is given by $$ \begin{aligned} p(1,1) &=\frac{1}{8}, & p(2,1) &=0, & P(3,1) &=\frac{1}{24}, 1 p(1,2) &=\frac{1}{4}, & p(2,2) &=\frac{5}{24}, & P(3,2) &=\frac{1}{16}, " p(1,3)=\frac{1}{16}, & p(2,3) &=0, & P(3,3) &=\frac{1}{4} . \end{aligned} $$ Find (a) $p_{X \mid Y}(3 \mid 1) ;$ (b) $\mathbb{E} [X \mid Y=2]$ and (c) $F_{Y \mid X}(2 \mid 1)$ SP. PB. 102