Overview

A random variable is a real valued function defined on a set of possible outcomes called a probability space.

Topics

• Cumulative Distribution Function
• Probability Density Function
• Sum of Random Variables

Comparison of Density and Cumulative

The following plots out the probability density and cumulative probability function for the normal distribution.

Formal Definition

The exact technical requirements for a function to be considered a random variable is that the function is measurable. This requirement ensures that a probability can be assigned to events which represent specified values of the random variable. For example, it can be asked what the probability of a given value or range of values of the random varialbe is.