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
• \(0≤F\left( x \right)≤1\)
• \(\lim_{x→∞} F\left( x \right)=1\)
• \(\lim_{x→-∞} F\left( x \right)=0\)