Suppose $X$ and $Y$ are continuous uniform random variables. If $X \sim U[a,b]$, $Y \sim U[c,d]$ and $[c,d] \subset [a,b]$ find the probability that a random $X$ value is greater than a random $Y$ value.
I think maybe that's problem can resolve drawing a rectangule, but a i need help with that
When you draw the arbitrary rectangle, with vertices $(a,c), (a,d), (b,c), (b,d)$ and draw in the line $y=x$, we want to find the area of the region below the line inside the rectangle. If you draw this region out, you find that the region is a trapezoid with vertices $(c,c), (b,c), (d,d),$ and $(b,d)$
The problem simplifies down to finding the ratio of the area of the trapezoid to the area of the rectangle.