Chapter 10.1, Problem 38E

(a)

To determine

The probability $P\left(0\le X\le 1;1\le Y\le 2\right)$ of a joint probability density function $f\left(x,y\right)=\frac{1}{12}\left(x+y\right)$ on a region $D=\left\{\left(x,y\right)|0\le x\le 2;1\le y\le 3\right\}$.

(b)

To determine

The probability $P\left(Y\ge 1;X+Y\le 3\right)$ of a joint probability density function $f\left(x,y\right)=\frac{1}{12}\left(x+y\right)$ on a region $D=\left\{\left(x,y\right)|0\le x\le 2;1\le y\le 3\right\}$.