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1) Let X and Y be random variables with a joint probability density f.pdf
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1) Let X and Y be random variables with a joint probability density function fX,Y. Let fY be the marginal distribution of Y. We define the conditional probability density of X given Y as fXY(xy)={fY(y)fX,Y(x,y)0iffY(y)=0iffY(y)=0. We then define E(XY=y)=xfXY(xy)dx. Suppose that fX,Y(x,y)={200x1andxy1otherwise (a) Find E(XY=y). (b) Find E(YX=x)..
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1) Let X and Y be random variables with a joint probability density f.pdf
- 1) Let X and Y be random variables with a joint probability density function fX,Y. Let fY be the marginal distribution of Y. We define the conditional probability density of X given Y as fXY(xy)={fY(y)fX,Y(x,y)0iffY(y)=0iffY(y)=0. We then define E(XY=y)=xfXY(xy)dx. Suppose that fX,Y(x,y)={200x1andxy1otherwise (a) Find E(XY=y). (b) Find E(YX=x).
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