Overview
On this page, we discuss the concept of the expected value (or “expectation“) of a discrete random variable and its properties.
Basic learning objectives
These are the tasks you should be able to perform with reasonable fluency when you arrive at your next class meeting. Important new vocabulary words are indicated in italics.
 Know the precise definition of the expected value of a discrete random variable, and be able to calculate the expected value of a discrete random variable from its probability mass function.
Advanced learning objectives
In addition to mastering the basic objectives, here are the tasks you should be able to perform after class, with practice:

Use the Law of the Unconscious Statistician and Linearity of Expectation to calculate the expected value of a random variable when appropriate.

Use indicator random variables and linearity to calculate expected values when appropriate.
To prepare for class

Watch the following video (by MIT OpenCourseWare) which introduces the expected value of a discrete random variable, and shows how to calculate this for some examples (including the socalled Bernoulli random variable, indicator random variables and the uniform distribution):
After class

Watch the following video (by MIT OpenCourseWare) which explains an important property of the expected value which is often called the Law of the Unconscious Statistician (LOTUS):

Watch the following two videos (by MIT OpenCourseWare) which explain & prove two important linearity properties of the expectation (you can ignore the second half of the second video for now):

Watch the following video (by Brendan Cordy) which shows an example of using linearity and indicator variables to calculate an expected value: