3.3 Properties of CDFs
A CDF, say \(F_X(x)\), has these properties:
- \(\displaystyle\lim_{x\to -\infty} F_X(x) = 0\).
- \(\displaystyle\lim_{x\to\infty} F_X(x) = 1\).
- \(F_X(x)\) is a non-increasing, right-continuous function.
- \(\Pr(a<X<b) = F_X(b) - F_X(a)\) when \(X\) is continuous.