Find the expected value

The question I am having difficulties with go like this:

Given a pdf:

f(x) = y/2*{exp(-yx)+bexp(-byx)}

find E(X) and E(X^2)

Now with E(X), this equals the intregral of x*f(x). I tried solving this using integration by parts and got -1/(2y)+1/(yb), which I don't think is right.

Also with E(X^2), i tried solving the intregral of x^2*f(x) but I get stuck trying to do the calculations.

I think I am on the right track with what I am doing but I just can't seem to do the calculations right.

Your probability density function is insufficiently defined. Are x and y positive? What integration limits have you used? I do not think it is reasonble for you to find the entiderivative of that expression, certainly not after adding the 'x' or 'x^2".

More information.

Sorry. I forgot to say that x>0, y>0 and 0<=b<1.

When you want to find the expected value, do you just integrate from 0 to infinity?

Integrate? If you can, but you'll have a tough time with that one.