Expected Profit

#1
This question is really confusing me:

The annual profit Y(in $100,000) can be expressed as a continuous function of drug demand x(in 1,000): Y(x) = 2(1-e^(-2x)). Suppose the demand for their drug has the probability function: f(x)= 6e^(-6x), x>0. Find the company's expected annual profit.

I cant figure out how to even get started. How are the 2 functions connected? How exactly is expected profit calculated?

Thanks a lot if someone can help.
 

Dason

Ambassador to the humans
#6
By taking a limit. Technically what you do is figure out what the integral is from 0 to c in closed form. Then you take the limit of that as c goes to infinity. You'll see that it converges in this case so there isn't an issue. They're called improper integrals but they're used all the time.