Talk:Mean dependence

Notation

Is ƒ₁(x) a notation that needs to be linked? RJFJR (talk) 23:03, 30 April 2017 (UTC)[reply]

I've fixed it. Loraof (talk) 22:19, 2 August 2017 (UTC)[reply]

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)[reply]