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Given a Probability Density Function ${f_X}(x)$, how can I prove that ${f_X}(x)$ is a valid distribution function? I already known that ${f_X}(x) \ge 0$ and $\int\limits_{ - \infty }^\infty {{f_X}(x)dx = 1} $ for all $x$.

Thanks!

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    If it is a Borel function, then you're safe.2012-11-15

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