Question: LetXandYbe two jointly continuos random variables with the joint PDF 6xy,if 0

LetXandYbe two jointly continuos random variables with the joint PDF

6xy,if 0

0,otherwise.

a) Find the marginal probability density functionsfX(x) andfY(y). b) AreXandYindependent?

c) Find the conditional PDF ofXgivenY=y,fX|Y(x, y).

d) Find the conditional expectationE(X|Y=y) for 0y1. e)FindVar(X|Y=y)for0y1.

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