It seems you only need E(300-2X)=300-2(50)
Y=aX+b is always a uniform rv, if X is.
Suppose that a company will incur a loss X that is uniformly distributed between 0 and 100. The company will pay a bonus to its employees that is uniformly distributed from 0 to 300−2X. What is the expected value of the bonus paid?
Since X~Uniform(0,100), the pdf would be f(x) = 1/100, 0 < x < 100. For Y = 300 - 2X, I used the change of variables formula to get f(y) = 1/200. I assume this problem must have something to do with the conditional mean, E(Y|X=x), but for that I would need a joint pdf f(x,y) and X = some value, which I'm not sure how I'd find. Where should I go from here?
I understand what you are saying, but I was thinking about this some more. Since the bonus (Y) is uniformly distributed between 0 and 300-2X, the pdf of Y|X should be f(y|x) = 1 / (300-2x). Then the expected value of Y|X should be E(Y|X) = (300-2x)/2 = 150 - x. So if I know the expected value of X is 50, couldn't I just plug it in to get E(Y|X=50) = 150 - 50 = 100?