= Solution
Let $Y_1,Y_2,\ldots$ be real <independent and identically distributed random variables> with finite <expected value> $\mu$ and <variance> $0<\sigma^2<\infty$. The <central limit theorem> states
$$
\boxed{\frac{\sum_{k=1}^nY_k-n\mu}{\sigma\sqrt n}\xrightarrow dN(0,1).}
$$
Equivalently, the <cumulative distribution functions> of these normalized sums converge at every real point to the <standard normal distribution function>. The theorem itself does not require a finite moment-generating function.
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