- #1
estebanox
- 26
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Consider three jointly normally distributed random variables X,Y and Z.
I know that in the Gaussian case E[Z | X,=x Y=y]=xßZX;Y +yßZY;X
where ßZX;Y notes the regression coefficient of Z on X conditional on Y (and ßZY;Xis analogously defined).
Is the following derivation correct?
E[Z| X>x, Y<y] = E [ E[Z | X,Y] | X>x, Y<y]
=ßZX;Y E[X | X>x, Y<y]+ßZY;X E[Y |X>x, Y<y]
I know that in the Gaussian case E[Z | X,=x Y=y]=xßZX;Y +yßZY;X
where ßZX;Y notes the regression coefficient of Z on X conditional on Y (and ßZY;Xis analogously defined).
Is the following derivation correct?
E[Z| X>x, Y<y] = E [ E[Z | X,Y] | X>x, Y<y]
=ßZX;Y E[X | X>x, Y<y]+ßZY;X E[Y |X>x, Y<y]