Cumulative distribution function
In probability theory, a cumulative distribution function F(x) of a probability density function say f(x) is a real valued and continuous function whose value is the proportion of probability values of a variable which occur on the part real line up and including the value of that variable; i.e.,
Due to the properties of the probability density function f(x), the cumulative distribution function F(x) will have the following properties:
(1) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle F(x) \geq 0 }
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \forall x }
inside its domain of support.
(2) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle F(\infty) = 1 }
, i.e., finitely convergent (to unity by convention).
(3) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle F(a) \leq F(b) }
for a<b, i.e., is non-decreasing
If the domain of the variable is finite, then the argument in equation (2) above should be the upper bounds.