$$E[X-E[X]]=0$$
Proof
To proof the expression, we use the property of \(E[aX+b]=aE[X]+b\).
If we let \(a=1\) and \(b=-E[X]\), we obtain
$$E[X-E[X]]=E[X]-E[X]=0$$
Welcome to Math World!
$$E[X-E[X]]=0$$
To proof the expression, we use the property of \(E[aX+b]=aE[X]+b\).
If we let \(a=1\) and \(b=-E[X]\), we obtain
$$E[X-E[X]]=E[X]-E[X]=0$$