The way I see this problem, it is a mixed distribution where the given profit function Y is conditional on X:
and therefore to find E(Y) you need first to find marginal distribution and then go from there.
But I may be totally wrong!
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(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.
So do I have to start by doing ? I'm sure I have the upper bound wrong...
, 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. is not a pdf. We just have that , so in order to find Y's pdf, there's a change of variable to make in X's pdf