3.3 Properties of CDFs

A CDF, say $F_X(x)$, has these properties:

1. $\displaystyle\lim_{x\to -\infty} F_X(x) = 0$.
2. $\displaystyle\lim_{x\to\infty} F_X(x) = 1$.
3. $F_X(x)$ is a non-increasing, right-continuous function.
4. $\Pr(a<X<b) = F_X(b) - F_X(a)$ when $X$ is continuous.

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Copyright © Peter K. Dunn, 2021