Do these texts contradict eachother?

billym · #1 $Old$ November 4th, 2009, 11:12 AM

Do these two texts contradict each other?

Or does it mean that not all cases where E[Y | X] = E[Y] are independent, but if X and Y are independent, then E[Y | X] = E[Y] ?

statmajor · #2 $Old$ November 4th, 2009, 01:22 PM

Quote:

Originally Posted by billym $View Post$

Do these two texts contradict each other?

No, they do not

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Or does it mean that not all cases where E[Y | X] = E[Y] are independent,

Unless we know that X and Y are independent, E[Y | X] = E[Y] doesn't prove they are independent. E[Y | X] = E[Y] could be just a coincidence.

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but if X and Y are independent, then E[Y | X] = E[Y] ?

Yes, if X and Y are independent, X doesn't effect Y, and vice versa. Thefore E[Y | X] = E[Y]

Moo · #3 $Old$ November 4th, 2009, 01:26 PM

Quote:

Originally Posted by billym $View Post$

Or does it mean that not all cases where E[Y | X] = E[Y] are independent, but if X and Y are independent, then E[Y | X] = E[Y] ?

Yes, it means what you've just written.
It there would be this equivalence :

for any [some conditions over] f, E[f(Y)|X]=E[Y] <=> X and Y are independent.

So they do not contradict each other