There are many types of variables in mathematics. Some, called [i]deterministic variables[/i], have a predictible value given by a rule or relation. But in other cases, variables can depend on chance events. For example:[br][list][*]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.[/*][/list]Because of the element of chance in these variables, we cannot predict the exact value they will take when next measured.[br][br]But, we can often determine the possible values the variable can take, and assign them the probability of it occurring.[br][br][color=#0000ff]A [b]random variable[/b] uses numbers to describe the possible outcomes which could result from a random experiment.[/color]

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. [br][br]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.[br][br]X is not only a random variable, but a [b]discrete[/b] random variable.

[color=#0000ff]A [b]discrete random variable[/b] X has a set of distinct possible values.[/color][br][br]For example, X could be:[br][list][*]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.[/*][/list][br]A random variable can also be continuos, but we will talk about that later.