Let $X_i \quad$ be independent identically distributed Random Variables s.t. $E|X|^q < \infty$ ( some $q \in \mathbb{N} )$. When defining
$Y_i:= (X_i-\bar{X}_n)^q$
why is it true that $Y_i$ are iid for $i \in (1,..,n)$ ? Does subtracting the sample mean not introduce interdependence ?