# Cumulative distribution function

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Let $\mathbb{T}$ be a time scale. Let $f \colon \mathbb{T} \rightarrow \mathbb{R}$ be a probability density function. The following function is called the cumulative distribution function (or cdf) of $f$: $$F(x) = \displaystyle\int_0^x f(t) \Delta t.$$

# References

Probability theory on time scales and applications to finance and inequalities by Thomas Matthews