Google Classroom
GeoGebraGeoGebra Classroom

Discrete Random Variables

Definition of Random Variable

There are many types of variables in mathematics. Some, called deterministic variables, have a predictible value given by a rule or relation. But in other cases, variables can depend on chance events. For example:
  • the number of players in a football teem that will score a goal in the next match,
  • the time it will take you to travel to school tomorrow,
  • the sum of the values when three dice are rolled.
Because of the element of chance in these variables, we cannot predict the exact value they will take when next measured. But, we can often determine the possible values the variable can take, and assign them the probability of it occurring. A random variable uses numbers to describe the possible outcomes which could result from a random experiment.

This is a throwing dice simulator. n represents a given thrown of the dice, and X is a variable that takes the value of the dice in each thrown.

In this applet, you can simulate up to 1000 throws of a dice. Move the slider n to get a new result, or press the play button to throw it fast. X is a random variable, as its value depends on a chance event. We can't predict its actual value each time, but we know it is going to be an integer number between 1 and 6. X is not only a random variable, but a discrete random variable.

Discrete random variables

A discrete random variable X has a set of distinct possible values. For example, X could be:
  • the numbers from the faces of a dice, so X could take the values 1, 2, ..., 6
  • the number of defective light bulbs in a purchase order of 50, so X could take the values 0, 1, 2,... , 50
  • the number of e-mails a person gets a day, so X could take the values 0, 1, 2,... up to infinity. In this course we will not consider variables like this.
A random variable can also be continuos, but we will talk about that later.