Before we give a definition of discrete random variables, let’s define random variables.

A **random variable** is a variable with exactly 1 numerical value and this value is determined by the result of a random experiment.

For example, the number of vehicles someone owns is a random variable. To find out, you need to randomly select people and ask. For example, suppose you ask 200 people, and 40 people say they don’t own a car, 100 say they own 1, and 60 say they own 2.

Let x be the number of vehicles owned by a randomly selected person. Then x could be 0, 1, or 2 based on our result.

Since the value of x depends on the result of a random experiment or a random survey of people, x is referred to as a random variable or random variable.

What is a **discrete random variable** ?

A random variable that takes on different and countable values is called *discrete random variable*.

Why are the values **clear**? In the example above, someone can own either 0 vehicle, 1 vehicle, or 2 vehicles. These values are clearly different or different. 1 is not equal to 0, 1 is not equal to 2, and 0 is not equal to 2.

Why are the values **countable**? This is because we can count them: 0, 1 and 2. There are 3 different values and we were able to count without any problems.

## Other examples of discrete random variables

The number of customers who visit a store at any given hour.

The number of televisions a person owns.

The number of tails obtained by flipping a coin three times.

The number of car accidents that occur in a city during a week.

Note that the number of customers visiting the store gives different values. The number of visitors could be 0, 1, 2, 3, 4, 5, … and again we can still count.

Also note that if you toss a coin three times you can get 0 teal, 1 number, 2 number, or 3 number.

In our example above for the number of vehicles someone owns, we found 3 different values {0, 1, 2}. This is a simple count as we are dealing with a finite number of values.

A random variable can still be discrete with an infinite number of values as long as we can count those values or make a list.

For example, let x be the number of customers who visit a store forever

This list is very, very big, but the list is still countable if you could live forever. This will take you forever to count, of course, but you will be able to count if you never die!

A discrete random variable has either a finite number of values or a countable number of values, even if it takes forever to count.