A random variable $X_n$ is asymptotically normal if there exists sequences $\{a_n\}$ and $\{b_n\}$ of real numbers such that $\frac{X_n - a_n}{\sqrt{b_n}} \overset{d}{\to} N(0,1)$ We write $X_n \overset{asymp}{\sim}N(a_n, b_n)$