3.2 Random Variables & Distributions
Equip yourself with the tools to quantify and understand chance.
Random Variables
Distributions
Random Variable Applications
Definition
Density Functions
Joint Distributions
Expected Value Definition and Properties
Expected Value Calculations
Conditional Expectation
Linearity of Expectation
Indicator Variables
Variance Definition and Properties
Variance and Standard Deviation
Covariance
Uniform Discrete Distribution
Bernoulli Distribution
Binomial Distribution
Geometric Distribution
Poisson Distribution
Applications of Discrete Distributions
Definition
Density Functions
Joint Distributions
Expected Value and Variance
Normal Distribution
Exponential Distribution
Gamma Distribution
Log-Normal Distribution
Course description
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.
Topics covered
- Bernoulli Trials
- Binomial Distribution
- Conditional Expectations
- Covariance
- Density Functions
- Discrete and Continuous Distributions
- Discrete and Continuous Random Variables
- Expected Value
- Joint Distributions
- Normal Distribution
- Standard Deviation
- Variance
Prerequisites and next steps
You'll need an understanding of basic algebra, including functions, as well as fundamental probability. Calculus will be helpful for later chapters on continuous random variables.
Prerequisites
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4.1 Applied Probability
Tap into a framework for understanding the world around us, from sports to science.
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