If the joint probability density of $X$ and $Y$ is given by
$$f(x,y)=\left\{\begin{matrix} \frac{1}{y},0<x<y,0<y<1 & & & \\ 0, elsewhere& & & \end{matrix}\right.$$
Find $P(X+Y>\frac{1}{2})$
How should I graph it so that I could know what to integrate? Hope someone can provide a graph with explanations. Thanks in advance.
$\{(x,y): 0<x<y<1, x+y>1/2\}$ is the interior of the polygon: $(1/4,1/4)(0,1/2)(0,1)(1,1)$
Its the upper-left section of the unit square cut by the lines $y=x, y=1/2-x$ .