Final answer:
A continuous probability function is a function that describes the probabilities of outcomes for a continuous random variable. It is represented by a probability density function (pdf) and has two rules: f(x) > 0 for all x and the total area under the curve is equal to one.
Step-by-step explanation:
A continuous probability function is a function that describes the probabilities of outcomes for a continuous random variable. It is represented by a probability density function (pdf), denoted as f(x). The two rules that apply to any continuous probability function are:
- The pdf f(x) is always greater than zero for all values of x.
- The total area under the curve of f(x) is always equal to one.
For example, consider the pdf f(x) = 2x for 0 < x < 1. The function satisfies both rules, as it is always greater than zero and the area under the curve from 0 to 1 is equal to one.