Solution (source code)

= Solution

The <delta method> gives
$$
\sqrt n\bigl(\varphi(\widehat\psi_n)-\varphi(\psi)\bigr)
\Rightarrow N\left(0,\,[\varphi'(\psi)]^2v\right).
$$
If $\varphi'(\psi)=0$, this denotes the degenerate distribution at zero.