From random outcomes to probability distributions
Maps outcomes to numbers
Probability of each value
Long-run average
Spread of distribution
Discrete random variables transform random experiments into mathematical objects we can analyze. From coin flips to customer arrivals, model uncertainty, calculate probabilities, and make predictions with the fundamental distributions that power statistics and data science.
Master probability distributions and their applications
All sections are accessible - follow the numbered sequence for the best learning experience
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Build formulas step-by-step
Build discrete distribution formulas interactively. Click on each part to understand why it's there and how it works.
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From outcomes to numbers
Random variables map outcomes to numerical values. Build intuition through interactive spatial visualization.
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Center and spread of distributions
Fundamental measures of distributions. Calculate expected values and understand variability through interactive examples.
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Linear and function transformations
Transformations affect expectation and variance. Explore the rules for linear and non-linear transformations.
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Counting successes in trials
Explore the most important discrete distribution. Model repeated independent trials with interactive simulations.
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Waiting for the first success
Model the number of trials until the first success. Understand memoryless property through interactive examples.
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Waiting for multiple successes
Generalize the geometric distribution to model waiting for r successes. Explore through interactive visualizations.
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Modeling rare events
Distribution of rare events in continuous time or space. See connections to binomial and exponential.
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Choosing the right model
When to use each distribution through real-world scenarios. Practice distribution selection.
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Start with fundamentals to understand the core concepts
Apply concepts to real-world data to reinforce understanding
Learn when and how to apply each concept effectively