Math Help - conditional probability

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??

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

I assume you typoed and you meant to say
(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?