Point probability of a sample mean

Let $\{X_n\}_{n\ge1}$ be a sequence of i.i.d. random variables having common probability density function

$$f(x)=\begin{cases}xe^{-x}, & x\ge0,\ 0, & \text{otherwise.}\end{cases}$$

Let $\overline X_n=\frac1n\sum_{i=1}^nX_i$, $n=1,2,…$. Then $\lim_{n\to\infty}P(\overline X_n=2)$ equals