Random Variables

In Week 1, a variable was defined a variable as a characteristic or attribute that can assume different values.

Various letters of the alphabet, such as \(X\), \(Y\), or \(Z\), are used to represent variables. Since the variables in this chapter are associated with probability, they are called random variables.

A Random Variable is a variable whose values are determined by chance.

Just like the variables of Week 1, random variables also come in two flavors: Discrete and Continuous

Discrete Random Variable have a finite number of possible values or an infinite number of values that can be counted.

Example(s): the number of joggers in Riverview Park each day and the number of phone calls received after a TV commercial airs are examples of discrete variables, since they can be counted.

Continuous Random Variable can assume all values in the interval between any two given values

if the temperature goes from \(62^\circ\) to \(78^\circ\) in a 24-hour period, it has passed through every possible number from 62 to 78.

Key: Continuous random variables are obtained from data that can be measured rather than counted.