Journey from discrete to continuous probability distributions
Probability per unit interval
Finding area under curves
The bell curve
Waiting time distribution
Move beyond counting to measuring. Continuous distributions open up a world of infinite possibilities, from the ubiquitous normal distribution to exponential waiting times. Master integration, probability density, and the tools that power modern statistics and machine learning.
From discrete counts to continuous measurements
All sections are accessible - follow the numbered sequence for the best learning experience
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Build formulas step-by-step
Master continuous distribution formulas by building them interactively. Click on each part to understand why it's there and how it works.
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From discrete to continuous
Make the conceptual leap from discrete to continuous distributions. Understand probability density and area under curves.
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PDFs and integration
Master probability density functions and calculate probabilities through integration. Interactive visualizations make calculus intuitive.
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Continuous E[X] and Var(X)
Calculate expected values and variance for continuous distributions using integration. Build intuition through visualizations.
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The bell curve and z-scores
Master the most important continuous distribution. Learn z-scores, empirical rule, and normal table lookups through interactive tools.
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Modeling waiting times
Model continuous waiting times with the exponential distribution. Explore memoryless property and connections to Poisson.
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Generalized waiting times
Extend exponential to model waiting for multiple events. Master shape and scale parameters through visualization.
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Multiple random variables
Extend to multiple continuous variables. Master joint PDFs, marginal distributions, and conditional distributions.
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Central Limit Theorem preview
See how discrete distributions approach normal for large n. Apply continuity correction for better approximations.
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Interactive integration tool
Master double integrals for joint distributions. Visualize numerical integration step-by-step with different methods and see how probabilities are calculated over regions.
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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