- #1
libragirl79
- 31
- 0
Hi,
I am trying to show that if the E[W|X]=0 then the Cov (W,X)=0.
Using the def of variance, and given that E[W] is zero,
I get that Cov is equal to: E[WX]-E[W * E(X)]
using conditional expectation:
E [E(WX|X)] -E[x]E[W]= E[X E[W|X]]-E[X]E[E(W|X)]=0
I am not sure if this transition (in red) is ok.
Thanks!
I am trying to show that if the E[W|X]=0 then the Cov (W,X)=0.
Using the def of variance, and given that E[W] is zero,
I get that Cov is equal to: E[WX]-E[W * E(X)]
using conditional expectation:
E [E(WX|X)] -E[x]E[W]= E[X E[W|X]]-E[X]E[E(W|X)]=0
I am not sure if this transition (in red) is ok.
Thanks!