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Let continuous random variables X, Y be jointly continuous, with the following joint distribution fXY​(x,y) =...

Let continuous random variables X, Y be jointly continuous, with the following joint distribution fXY​(x,y) = e-x-y ​for x≥0, y≥0 and fXY(x,y) = 0 otherwise​.

1) Sketch the area where fXY​(x,y) is non-zero on x-y plane.

2) Compute the conditional PDF of Y given X=x for each nonnegative x.

3) Use the results above to compute E(Y∣X=x) for each nonnegative x.

4) Use total expectation formula E(E(Y∣X))=E(Y) to find expected value of Y.

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