1.2 Types of random variables

The most common types of rvs are:

  • Discrete rvs, such as gender, number of siblings, number of coin tosses till a head appears, etc.

    A discrete rv is a rv whose possible values are a finite set, or else can be listed in an infinite sequence (with a first, second, third, etc., element).

  • Continuous rvs such as height, weight, time to complete a task, etc.

    For a continuous rv, there are an infinite number of possible values in an interval (or in intervals) on the real number line. So, for example, an infinite number of heights exist between \(160\)cm and \(170\)cm (though we conveniently round to the nearest centimetre).

  • Mixed rvs that are partially discrete and partially continuous.

    Examples include rainfall: no rain means an exact zero (the discrete part), but when rain falls the amount is continuous.

Example 1.5 (Discrete rv) In Example 1.2, \(C\) is a discrete rv with a finite number of outcomes.

In Example 1.3, \(X\) is a discrete , with no theoretical upper limit, and so an infinite number of outcomes.

In Example 1.4, \(H\) is a continuous rv, with no theoretical upper limit, and no theoretical lower limit (given that a height of 0cm so far from actual heights).