Continuous Random Variables

Summary :

This chapter distinguishes continuous random variables, which are measured, from discrete random variables, which are counted, using examples such as the length of a phone call or a person's SAT score. It covers continuous probability density functions in general, and studies the uniform and exponential distributions as two specific continuous models.

Measured values versus counted values

The chapter uses paired examples, such as the number of miles driven, which is counted and discrete, against the actual distance driven, which is measured and continuous, to teach students how the same underlying quantity can be treated as either a discrete or a continuous random variable depending on exactly how it is defined.

Continuous probability density functions

Students learn to recognize and understand continuous probability density functions in general, building on the idea that probability corresponds to the area under a curve rather than to the height of a bar, extending the relative-frequency reasoning already familiar from histograms into the continuous setting.

The uniform and exponential distributions

The chapter studies two named continuous distributions in turn: the uniform distribution, where every outcome in an interval is equally likely, and the exponential distribution, and asks students to recognize each one and apply it appropriately to a described situation, building toward the normal distribution introduced later in the course.