# Expected Profit

#### stat_student001

##### New Member
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.

#### stat_student001

##### New Member
Calculation of expectation of a continous variable is given here:
http://en.wikipedia.org/wiki/Expected_value
See under E[g(X)]. Set g(X) = Y(X).
Ah ok, so it would be the integral of Y(x)f(x). But what would be the bounds? The lower bound would be 0, but the upper bound would be infinity? How would you compute the annual profit then? Thank you!

#### Dason

The lower bound would be 0, but the upper bound would be infinity?
Yup.
How would you compute the annual profit then? Thank you!
What exactly is the problem? Computing that integral gives you the expected annual profit.

#### stat_student001

##### New Member
Yup.

What exactly is the problem? Computing that integral gives you the expected annual profit.
I'm sorry, I could be being really dumb right now, but how can you calculate an integral with one of the bounds being infinity, and get a numerical answer?

#### Dason

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.

#### stat_student001

##### New Member
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.
Oh, i see. thanks a lot for your help