= Solution
{c}
The <central limit theorem> states that if $W_1,W_2,\ldots$ are <independent and identically distributed random variables> with finite <mean> $\mu$ and finite positive <variance> $\sigma^2$, then
$$
\boxed{\frac{\sum_{i=1}^nW_i-n\mu}{\sigma\sqrt n}\xrightarrow{d}N(0,1).}
$$
Here the arrow means <convergence in distribution>: for every real $z$, the <probability> that the expression on the left is at most $z$ tends to $\Phi(z)$, the <standard normal distribution function>. If $\sigma^2=0$, the variables equal $\mu$ <almost surely> and their <sample mean> is exactly $\mu$.
Back to article page
