Cumulative distribution function
- $F: \mathbb{R} \rightarrow \mathbb{R}$,
Definition
$F$ is said to be non increasing if
\[\forall x < y, \ F(x) \ge F(y) .\]$F$ is said to be non decreasing if
\[\forall x < y, \ F(x) \le F(y) .\]■
Definition
- $F:\mathbb{R} \rightarrow [0, 1]$,
$F$ is said to be cumulative distribution function if
- $F$ is non deacresing
- $F$ is right continutous left limit
- $F(\infty) = 1$,
- $F(-\infty) = 0$,
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