Homework Soursewhy PY 1 X x EY X xSolutionBy the law of total expectat
why
P{Y = 1 |X = x} = E{Y | X = x}.
Solution
By the law of total expectation, E(XY)=E[E(XYX=x)]=…E(XY)=E[E(XYX=x)]=…
Now, because X=xX=x is a constant and by linearity of expectation,
=E[xE(Y|X=x)]=E[xE(Y|X=x)]
So we got that no matter what X,YX,Y are: E(XY)=E[xE(Y|X)]E(XY)=E[xE(Y|X)]. by this we can say that
P{Y = 1 |X = x} = E{Y | X = x}.is true
![why P{Y = 1 |X = x} = E{Y | X = x}.SolutionBy the law of total expectation, E(XY)=E[E(XYX=x)]=…E(XY)=E[E(XYX=x)]=… Now, because X=xX=x is a constant and by line](/WebImages/33/why-py-1-x-x-ey-x-xsolutionby-the-law-of-total-expectat-1097490-1761579130-0.webp "why P{Y = 1 |X = x} = E{Y | X = x}.SolutionBy the law of total expectation, E(XY)=E[E(XYX=x)]=…E(XY)=E[E(XYX=x)]=… Now, because X=xX=x is a constant and by line")
