Let $X_1,X_2,...,X_n$ be i.i.d such that
$$\mathbb{E}(X_1)=u$$ and $$Var(X_1)=\sigma^2$$.
Let $X_1',X_2',...,X_n'$ be i.i.d with the same distribution as $X_1,X_2,...,X_n$ but independent of them.
Let's assume that $\mathbb{E}(|X_1|^j)<∞$ and $\mathbb{E}(|X_1-u|^j)<∞$
show that $\mathbb{E}|\bar X-u|^j$ $\le$ $\mathbb{E}|\bar X-\bar X'|^j$.
Could some one please help me with this or suggest me some materials to read through? Much appreciated.