Another way to specify the distribution of a Random variable. The difference between PMFs and CDFs is that PMFs are only defined for discrete variables, while CDFs are defined for *all* random variables. Therefore, it is usually only used in the context of continuous variables.

For discrete variables, the CDF would simply be a stepwise function.

Given a random variable $X$, the CDF is given by $F_{X}$ where $F_{X}(x)=P(X≤x)$.

Also see Integrating the PDF to get the CDF.

## Properties of valid CDFs

A CDF $F$ obeys the following properties:

**Increasing:**if $u_{1}≤u_{2}$, then $F(u_{1})≤F(u_{2})$. Basically, the CDF is*always*increasing with respect to $u$.**Right-continuous:**for any real number $a∈R$, $lim_{u→a_{+}}F(u)=F(a)$.- $lim_{u→−∞}F(u)=0$ and $lim_{u→∞}F(u)=1$.