CDF, cumulative distribution function

Summary

• Given: A (real-valued) random variable $X$ .
• The cumulative distribution function $F:R→[0,1]$ is defined as

$$F(x)=P(X≤x)$$

Properties of the CDF function:

• $F$ is an increasing function
• $0≤F\left( x \right)≤1$
• $\lim_{x→∞} F\left( x \right)=1$
• $\lim_{x→-∞} F\left( x \right)=0$