A First Course in Statistics, 12th Edition

4.4 Probability Distributions for Continuous Random Variables

The graphical form of the probability distribution for a continuous random variable x is a smooth curve that might appear as shown in Figure 4.13. This curve, a function of x, is denoted by the symbol f(x) and is variously called a probability density function, a frequency function, or a probability distribution.

The areas under a probability distribution correspond to probabilities for x. For example, the area A beneath the curve between the two points a and b, as shown in Figure 4.13, is the probability that x assumes a value between a and $b(a<x<b).$ Because there is no area over a single point, say, $x=a$, it follows that (according to our model) the probability associated with ...