construct three random variables X Y Z so that
E(X|Y=y) , E(X|Z=z) are both constant whilst E(X|Z=x,Y=y) isnt a constant??
not really sure where to go with this??
I assume you typoed and you meant to sayconstruct three random variables X Y Z so that
E(X|Y=y) , E(X|Z=z) are both constant whilst E(X|Z=x,Y=y) isnt a constant
(X|Y=y) , E(X|Z=z) are both constant whilst E(X|Z=z,Y=y) isnt a constant
Let Y,Z be independant bernoulli variables. with p=0.5 for both.
Define:
So
(by analogy)
But consider
...etc. Obviously not constant so i wont do the other two cases.
That establishes the required properties. Not bad for an economist, eh?