Probability of $(X \leq 2Y)$ $X$ and $Y$ are independent and their probability density functions are
$$f_X(t)=f_Y(t)=\left\{\begin{array}{l} e^{-t},\:\text{if $t \geq 0$;} \\ 0,\:\text{otherwise.}\end{array}\right.$$
$P(X \leq 2Y)$=? (The probability of $X \leq 2Y$)

Because $X$ and $Y$ are independent, $f_{X,Y}(s, t) = e^{-s}e^{-t} = e^{-(s+t)}$, $s, t > 0$. 
Find the region where $X \leq 2Y$ and integrate appropriately.
