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test
$$ S_n = \sum_{i=1}^n X_i, $$

$$ P(X_i=1) = P(X_i=-1) = \frac{1}{2}. $$

$$ \lim_{n \to \infty} P(S_n < x \sqrt{n}), x \in \mathbb{R}. $$

$$ F(x) = \left\{\begin{matrix} 0,  & x < 1 \\ 1/6, & 1 \le x < 2 \\ 1/3, & 2 \le x < 3 \\ 1/2, & 3 \le x < 4 \\ 3/4, & 4 \le x < 5 \\ 1,  & x \ge 5 \end{matrix}\right. $$

$$ P(1.5 \le X \le 4.5). $$