# 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

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

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 **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:
x=0,1,2,3,… - The number of students who were protesting the tuition increase last semester:
x=0,1,2,3,…. Notice thatx could become very large. - The number of applicants who have applied for the vacant position at a company:
x=0,1,2,3,… - The number of typographical errors in a rough draft of a book:
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:
x>0 , wherex is the time. - The depth of oil drilling to find oil:
0<x<c , wherec is the maximum depth possible. - The weight of a truck in a truck weighing station:
0<x<c , wherec is the maximum weight possible. - The amount of water loaded in a
12−ounce bottle in a bottle filling operation:0<x<12.

## 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**.

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