# 4.1: Two Types of Random Variables

**At Grade**Created by: CK-12

## Learning Objectives

- Learn to distinguish between the two types of random variables: continuous and discrete.

The word discrete means countable. For example, the number of students in a class is countable or discrete. The value could be \begin{align*}2, 24, 34,\end{align*}

However, if we are measuring the tire pressure in an automobile, we are dealing with a continuous variable. The air pressure can take values from \begin{align*}0\end{align*}

One way of distinguishing discrete and continuous variables is between any two values of a continuous variable, there are an infinite number of other valid values. This is not the case for discrete variables; between any two discrete values, there are an integer number \begin{align*}(0, 1, 2, \ldots)\end{align*}**countable** values since you could count a whole number of them.

## Discrete Random Variables and Continuous Random Variables

Random variables that assume a *countable number of values* are called discrete.

Random variables that can take any of the *countless number of values* are called continuous.

**Example:**

Here is a list of discrete random variables:

- The number of cars sold by a car dealer in one month: \begin{align*}x = 0, 1, 2, 3, \ldots\end{align*}
x=0,1,2,3,… - The number of students who were protesting the tuition increase last semester: \begin{align*}x = 0, 1, 2, 3, \ldots.\end{align*}
x=0,1,2,3,…. Notice that \begin{align*}x\end{align*}x could become very large. - The number of applicants who have applied for the vacant position at a company: \begin{align*}x = 0, 1, 2, 3, \ldots\end{align*}
x=0,1,2,3,… - The number of typographical errors in a rough draft of a book: \begin{align*}x = 0, 1, 2, 3, \ldots\end{align*}
x=0,1,2,3,…

**Example:**

Here is a list of continuous random variables:

- The length of time it took the truck driver to go from New York city to Miami: \begin{align*}x > 0\end{align*}, where \begin{align*}x\end{align*} is the time.
- The depth of oil drilling to find oil: \begin{align*}0 < x < c\end{align*}, where \begin{align*}c\end{align*} is the maximum depth possible.
- The weight of a truck in a truck weighing station: \begin{align*}0 < x < c\end{align*}, where \begin{align*}c\end{align*} is the maximum weight possible.
- The amount of water loaded in a \begin{align*}12-\;\mathrm{ounce}\end{align*} bottle in a bottle filling operation: \begin{align*}0 < x < 12.\end{align*}

## Lesson Summary

- A
**random variable**represents the numerical value of a simple event of an experiment. - Random variables that assume a
**countable**number of values are called**discrete**. - Random variables that can take any of the
**countless**number of values are called**continuous**.