I have attached the question on this thread.
I have managed to attain the following:
Yet I cannot obtain the fact that
I'm not sure how to derive this using my results.
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Consider that E[XY]=E[E[XY|X]]
Since you know the pdf of Y|X, you'll easily get the expectation. Then you'll get E[something with respect to X], which is again easy because you have the pdf of X.
And is follows that:
and then we just take the expectation
Am I correct?
Yes, it's correct.
A few remarks :
- are you aware of the properties of the conditional expectation that have been used ?
- in the pdf of X and of Y|X, you should respectively add that it's for x>0 and y>0
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