random variables

(1.7 hours to learn)


Random variables are the central object of probability theory. As their name implies, can be thought of as variables whose values are randomly determined. Mathematically, they are represented as functions on a sample space.


This concept has the prerequisites:

Core resources (read/watch one of the following)


Khan Academy: Probability and Statistics
Mathematical Monk: Probability Primer (2011)
Online videos on probability theory.
Other notes:
  • This uses the measure theoretic notion of probability, but should still be accessible without that background. Refer to Lecture 1.S for unfamiliar terms.


Supplemental resources (the following are optional, but you may find them useful)


Sets, Counting, and Probability
Online lectures on basic probability theory.
Location: Lecture "Random variables"


See also

  • Some important properties of random variables:
    • expected value , the value it takes "on average"
    • independence , i.e. one variable's distribution not depending on the other
    • variance , how much the value tends to deviate from the mean
    • entropy , a measure of the amount of uncertainty
    Some distributions of interest: