## 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.