$X$ 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 $X \leq 2Y$)

$X$ and $Y$ are independent and their probability density functions are $$f_X(t)=f_Y(t)=\left\{\begin{array}{ll} e^{-t},&\text{if $t \geq 0$;} \\ 0,&\text{otherwise.}\end{array}\right.$$

$P(X \leq 2Y)$=? (The probability of $X \leq 2Y$)

X and Y are independent and their probability density functions are

fX(t)=fY(t)=e^(-t) for t>=0. 0, otherwise.

P(X=<2Y)=? (The probability of X=<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 $X \leq 2Y$)