ABSTRACT
A probability distribution gives the frequency of occurrence of some variable. For example, the income distribution is summarized by a function F, where f(y) gives the fraction of the population with income at or below y. If a person is selected at random from the population, then the probability that the person will have income below y is F(y). Similarly, one may consider the age distribution, represented by G, so that G(a) is the fraction of people with age no larger than a, or a wage distribution where H(w) gives the proportion of people earning a wage no larger than w. Thus, a distribution provides information regarding the frequency of a certain characteristic or property in a population. Considering the income distribution, suppose a person is selected at random from the population and income recorded. At the selection process, let Y be the as yet to be determined income. This unknown number is called a random variable. The probability that the person selected at random will have an income below y is denoted P(Y ≤ y) and this is equal to f(y). In Section 18.2, random variables are introduced and briefly described. Intuitively, every distribution function describes the behavior of a random variable. Section 18.3 introduces the distribution function and its density.
