Definition 8

    Consider an observational variable which can be represented by a single real number. Let t denote the outcome of a single observation, while x is a real number. The frequency distribution F(x) is defined to be

$$F(x) = \text{Pr}(t \leq x).$$

It follows that

1. F(x) is a monotonic increasing, right-continuous function of x which is defined for all x.

2. $\lim_{x\to - \infty} = 0$ and $\lim_{x \to \infty} = 1$, where these limits may be attained at finite x.