Two Random Variables X and Y have a joint probability density function given by:
$$f(x,y) = \begin{cases} \left(\frac{2e^{-2x}}{x}\right) & \text{, $0 < y < x < ∞$} \\ \\ 0 & \text{, elsewhere} \end{cases}$$ Compute Cov( X, Y ):
I know that i need to calculate E(XY) and then proceed. But i am not being able to figure out the limits of the double integral. Please help me.
In order to find $\mathbb EXY$ you must calculate: $$\int\int xyf(x,y)dydx=\int_0^{\infty}\int_0^xxy\frac{2e^{-2x}}{x}dydx$$