Solution
= Solution
Let $\mu=\mathbb E[X_1]$ and $\sigma^2=\operatorname{Var}(X_1)\in(0,\infty)$. For <independent and identically distributed random variables>, the <central limit theorem> states
$$
\boxed{\frac{X_1+\cdots+X_n-n\mu}{\sigma\sqrt n}\xrightarrow{d}N(0,1).}
$$
The limit is the <standard normal distribution>. If the <variance> is zero, then $X_i=\mu$ <almost surely>; the centered sums are zero, and division by $\sigma$ is not defined.