Hi everyone. I've been studying up for the exam using Marcel Finan's study guide (found at http://ift.tt/1z0IN87), and I've been finding it... aggravating. I've been using it because it's free and because it provides plenty of problems for practice, but the guy is kind of crap at actually teaching the material. His examples don't really match the practice problems, and in many cases he failed to include essential concepts that I only learned about through lots of frantic Googling.
Pardon the rant; I just needed to get that out. Anyway, here are the two problems that are currently stumping me:
-Problem 1: Suppose that E(X|Y)=18-(3/5)Y and E(Y|X)=10-(1/3)X. Find E(X) and E(Y).
No idea where to begin on this one. The only methods I know to find conditional expectation require that you know the pdfs, and none are provided here.
-Problem 2: Let X be an exponential random variable with parameter 5, and Y a uniformly distributed random variable on (-3, X). Find E(Y).
I know that the pdf of X is 5e^-5x and the pdf of Y is 1/(X+3), and when I evaluated E(Y) using the range (-3,X) I ended up with (X-3)/2 as my answer. But I have no idea how to get that down to a specific numeric value. I would be able to do that if I knew their joint pdf (or the pdf of Y given X), but since they don't seem to be independent I have no idea how to do that.
Any help is appreciated.
Pardon the rant; I just needed to get that out. Anyway, here are the two problems that are currently stumping me:
-Problem 1: Suppose that E(X|Y)=18-(3/5)Y and E(Y|X)=10-(1/3)X. Find E(X) and E(Y).
No idea where to begin on this one. The only methods I know to find conditional expectation require that you know the pdfs, and none are provided here.
-Problem 2: Let X be an exponential random variable with parameter 5, and Y a uniformly distributed random variable on (-3, X). Find E(Y).
I know that the pdf of X is 5e^-5x and the pdf of Y is 1/(X+3), and when I evaluated E(Y) using the range (-3,X) I ended up with (X-3)/2 as my answer. But I have no idea how to get that down to a specific numeric value. I would be able to do that if I knew their joint pdf (or the pdf of Y given X), but since they don't seem to be independent I have no idea how to do that.
Any help is appreciated.
Two Questions (Conditional Expectation)
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