Hello,

Well, what is an improper integral to you ?Now when I evaluate that integral I get an improper integral. I've checked my work several times, but I can't seem to find what I'm doing wrong. Any suggestions?

Because it surely is an improper integral here, caused by the infinity boundary !

Now, I get the same problems as yours...

Setting , I get :

And we also can see that as x is very big.

And is a divergent Riemann integral !

My guess is that you should not calculate separately the expectations (you should know that you don't necessarily have , especially if there are integrals that don't exist), by using the

We proved in our class that if X and Y are bounded, then :

But I must say I don't know if it is the correct way...