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Let $f:[a, b] \rightarrow[a, b]$ be continuous. Show that $\frac{1}{n} \cdot \sum_{i=1}^{n} f((b-a) \cdot \operatorname{rand}()+a)$. $(b-a)$ converges to $\int_{a}^{b} f(x) d x$ as $n \rightarrow \infty$. This limit is the basic underlying principle of Monte-Carlo simulation.
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