The problem states:
X is a continuous uniform random variable on [0,50].
The conditional distribution of Y given X=x follows a uniform distribution on [0,15x].
Calculate E[y].
From this, we know the marginal density of x is $\frac {1}{15x}$.
But how do we find E[y]? I try to use the double expectation formula, E[Y] = E[E[Y|X]], but that's not the right approach.
I have spent over two days trying to solve this problem and I keep running into a brick wall. If anyone can help steer me in the right direction, I would greatly appreciate it.
The correct answer is 187.5. Thanks
Your approach seems ok to me: $E(Y|X)=15X/2$, and then calculate $E(15X/2)$.