given that p(y1,y2) = exp (-y2) for 0<y2<y1< infinity

how do i find the correlation coefficient for y1, y2?

i tried to use the formula for covariance and standard deviation to find the correlation but im stuck.

for cov(y1,y2) = <y1y2>-<y1><y2>
to find<y1y2> i tired to do double integral from o to y1 for y2 first and from 0 to infinity next for y1.( im not sure about the limits)

and then

<y1> and <y2>, i integrated p(y1,y2) from 0 to infinity ( again im not sure about the limits)

to find standard deviation,i know its the mean of y1 and y2 but im not sure how to find that