I would just like to check something regarding the delta method. After using the delta method to verify that,
$$ \sqrt(n)(g(X_n)-g(\mu)) \sim n(0,\sigma^2 [g\prime(\mu)]^2) $$
we cannot generally assume that assume that $E(g(X_n))=g(\mu)$, right? Under what conditions would this be true? Thanks.
