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?