Chapter 4.3, Problem 9E

Let X and Y have a uniform distribution on the set of points with integer coordinates in $S=\left\{\left(x,y\right):x\le x\le 7,x\le y\le x\le x+2\right\}$ [That is $f\left(x,y\right)=\frac{1}{24},\left(x,y\right)\in S$, and both x and are integers. Find

(a) $f_X\left(x\right)$

(b) $h\left(y|x\right)$.

(c) $E\left(Y|x\right)$.

(d) ${\sigma }_{Y|x}^2$

(e) $f_Y\left(y\right)$.