Talk:Mean dependence

Notation
Is ƒ1(x) a notation that needs to be linked? RJFJR (talk) 23:03, 30 April 2017 (UTC)
 * I've fixed it. Loraof (talk) 22:19, 2 August 2017 (UTC)

Reason for reverting alleged property
The following uncited alleged property was put in on 4 December 2011 by a single-edit anon:


 * "If X, Y are two different random variables such that X is mean independent of Y and Z = f(X), which means that Z is a function only of X, then Y and Z are mean independent."

I'm reverting this because the following is a counterexample: Let Y take on either of two values $$y_1$$ and $$y_2, $$ and say that if $$Y=y_1$$ then $$P(X=-1)=P(X=1)=1/2,$$ while if $$Y=y_2$$ then $$ P(X=-2)=P(X=2)=1/2;$$ and say $$Z=X^2.$$ Then $$E(X|y)=0$$ regardless of y, yet if $$Y=y_1$$ then $$P(Z=1)=1$$ so $$E(Z|y_1)=1 $$ while if $$Y=y_2$$ then $$P(Z=4)=1$$ so $$E(Z|y_2)=4.$$ Loraof (talk) 22:19, 2 August 2017 (UTC)