Random Variables & Distributions

The essential quantitative tools of chance.

Random variables and their distributions are the best tools we have for quantifying and understanding unpredictability. This course covers their essential concepts as well as a range of topics aimed to help you master the fundamental mathematics of chance.

Upon completing this course, you'll have the means to extract useful information from the randomness pervading the world around us.

Interactive
quizzes

28

Concepts and
exercises

275+
  1. 1

    Introduction

    What makes a variable random?

    1. Random Variables

      How do you quantify chance in a dicey world?

    2. Distributions

      Get a glimpse of how probabilities for random variables are computed.

    3. Random Variable Applications

      Explore some of the many real-world uses of random variables.

  2. 2

    Discrete Random Variables

    The language of random variables: independence, distributions, and more.

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      Definition

      What is a discrete random variable?

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      Density Functions

      Learn the process for assigning probabilities to random variables.

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      Joint Distributions

      Tackle problems with two uncertain quantities.

  3. 3

    Expected Value

    Know what outcome to expect when you're dealing with randomness.

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      Expected Value Definition and Properties

      Use averages to make predictions about random events.

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      Expected Value Calculations

      Gain hands-on experience with expectation value by exploring real-world applications.

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      Conditional Expectation

      Practice refining your expectations based on new information.

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      Linearity of Expectation

      Explore the most important feature of the expected value.

  4. 4

    Variance

    It's the mathematical way to describe how erratic your random variable is.

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      Variance Definition and Properties

      Develop an important means for assessing expected values.

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      Variance and Standard Deviation

      Calculate the spread of possibilities for a range of real-world scenarios.

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      Covariance

      Learn how to measure how two variables influence each other.

  5. 5

    Discrete Distributions

    Use these models to connect the theory to the real-world.

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      Uniform Discrete Distribution

      In this type of distribution, all outcomes are equally likely.

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      Bernoulli Distribution

      Investigate what surveys and coin flips have in common.

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      Binomial Distribution

      Apply the technique of Bernoulli trials to challenging probability problems.

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      Geometric Distribution

      Discover what it means for a distribution to have "no memory."

  6. 6

    Continuous Random Variables

    When the world gets continuous, calculus meets probability.

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      Definition

      Understand what it means for a random variable to have uncountably many outcomes.

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      Density Functions

      Extend the rules of probability to the infinite.

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      Joint Distributions

      Make sense of the uncertainty in two continuous random variables.

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      Expected Value and Variance

      Calculate predictions for uncountable outcomes and learn how to judge their accuracy.

  7. 7

    Continuous Distributions

    Model heights, stocks, or just about anything else with these distributions.

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      Normal Distribution

      Learn about a type of continuous distribution that you see pop up everywhere!

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      Exponential Distribution

      Discover why there's a common distribution for radioactivity and for winning the lottery.

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      Gamma Distribution

      Explore a distribution used by insurance companies the world over.

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      Log-Normal Distribution

      Learn to model stock market fluctuations in a simple way.