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# 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.

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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.

1. Included with

#### Definition

What is a discrete random variable?

2. Included with

#### Density Functions

Learn the process for assigning probabilities to random variables.

3. Included with

#### Joint Distributions

Tackle problems with two uncertain quantities.

3. 3

### Expected Value

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

1. Included with

#### Expected Value Definition and Properties

Use averages to make predictions about random events.

2. Included with

#### Expected Value Calculations

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

3. Included with

#### Conditional Expectation

Practice refining your expectations based on new information.

4. Included with

#### 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.

1. Included with

#### Variance Definition and Properties

Develop an important means for assessing expected values.

2. Included with

#### Variance and Standard Deviation

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

3. Included with

#### 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.

1. Included with

#### Uniform Discrete Distribution

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

2. Included with

#### Bernoulli Distribution

Investigate what surveys and coin flips have in common.

3. Included with

#### Binomial Distribution

Apply the technique of Bernoulli trials to challenging probability problems.

4. Included with

#### 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.

1. Included with

#### Definition

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

2. Included with

#### Density Functions

Extend the rules of probability to the infinite.

3. Included with

#### Joint Distributions

Make sense of the uncertainty in two continuous random variables.

4. Included with

#### 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.

1. Included with

#### Normal Distribution

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

2. Included with

#### Exponential Distribution

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

3. Included with

#### Gamma Distribution

Explore a distribution used by insurance companies the world over.

4. Included with

#### Log-Normal Distribution

Learn to model stock market fluctuations in a simple way.