Originally Posted by

**Canadian0469** Given two r.v.s Y1 and Y2 that have joint density fcn:

$\displaystyle f(y_1,y_2) = [1-\alpha[(1-2e^{-y_1})(1-2e^{-y_2})]]e^{-y_1-y_2}$ for 0 <= y_1, 0 <=y_2,

and 0 elsewhere

and $\displaystyle -1 \le \alpha \le 1$

I have to find $\displaystyle E(Y_1Y_2)$.

I did this by doing:

$\displaystyle \int^\infty_0 y_1e^{-y_1}[\int^\infty_0y_2[1-\alpha[(1-2e^{-y_1})(1-2e^{-y_2})]]e^{-y_2}\,dy_2] \,dy_1$

But I end up at a different answer than the final answer in the back of my text. The answer given in the back is:

$\displaystyle E(Y_1Y_2) = 1 - \alpha/4$