
Expected Profit
Sorry, I already asked a question today, but it would be awesome if someone could help me with this one, I feel like I'm close:
The annual profit Y(in $100,000) can be expressed as a continuous function of drug demand x(in 1,000): Y(x) = 2(1e^(2x)). Suppose the demand for their drug has the probability function: f(x)= 6e^(6x), x>0. Find the company's expected annual profit.
So do I have to start by doing http://s3.amazonaws.com/answerboard...9239628497.gif? I'm sure I have the upper bound wrong...

The way I see this problem, it is a mixed distribution where the given profit function Y is conditional on X:
$\displaystyle f_{YX}(yx)=2(1e^{2x})$
and therefore to find E(Y) you need first to find marginal distribution $\displaystyle f_Y(y)$ and then go from there.
But I may be totally wrong!

Hello,
$\displaystyle E[Y]=E[E[YX]]=E[E[2(1e^{2X})X]]=E[2(1e^{2X})]$, which is the formula alakaboom1 wrote.
As for the boundaries, it should rather be on the whole set of real numbers.
Then since f(x)=0 if x<0, the boundaries will indeed go from 0 to infinity.
Volga : there's something disturbing in what you wrote. $\displaystyle 2(1e^{2x})$ is not a pdf. We just have that $\displaystyle Y=2(1e^{2X})$, so in order to find Y's pdf, there's a change of variable to make in X's pdf :)
