A random variable is a single numerical value that indicates the outcome of a procedure. The concept of random variables is fundamental to the probability theory and was introduced by a Russian mathematician, Pafnuty Chebyshev, in the mid-nineteenth century.

Uppercase letters such as *X *or *Y* denote a random variable. Lowercase letters like *x* or *y* denote the value of a random variable. If *X* is a random variable, then *X* is written in words, and* x* is given as a number.

For example, let *X* = the number of heads you get when you toss three fair coins. The sample space for tossing three fair coins is TTT; THH; HTH; HHT; HTT; THT; TTH; HHH. Then,* x* = 0, 1, 2, 3. *X *is in words, and *x* is a number. Notice that for this example, the *x* values are countable outcomes.

Random variables can be of two types: discrete random variables and continuous random variables.

A discrete random variable is a variable that has a finite quantity. In other words, a random variable is a countable number. For example, the numbers 1, 2, 3,4,5, and 6 on a die are discrete random variables.

A continuous random variable is a variable that has values from a continuous scale without gaps or interruptions. A continuous random variable is expressed as a decimal value. An example would be the height of a student - 1.83 m.

*This text is adapted from* *Openstax, Introductory Statistics, section. 4 Introduction *

ABOUT JoVE

Copyright © 2024 MyJoVE Corporation. All rights reserved