From Chebyshev's inequality to Kolmogorov's axioms, the Russian and European schools turned probability from a gambler's calculus into a rigorous branch of mathematics.
0 / 25 LESSONS CONQUERED0%
TERRITORY BADGE
Reader of the Bell Curve
Complete all 25 lessons to claim
The Path Through
builds on XVII · New Machinery
Andrey Markov: Chains of Dependence
Biography
L673
Markov Chains: Memoryless Random Walks
Probability
L674
Markov Chains in Practice: From Text to Finance
Applied
L675
Pafnuty Chebyshev: Bounding Probability Without Distributions
Biography
L676
Chebyshev's Inequality: The Universal Bound
Statistics
L677
Andrey Kolmogorov: Making Probability Rigorous
Biography
L679
Kolmogorov's Axioms: The Rules of Probability
Probability
L680
Edgeworth: The Generalized Central Limit Theorem
Statistics
L686
Andrey Lyapunov: Stability and the CLT
Probability
L696
Emile Borel: Measure Theory and Probability
Probability
L697
Random Walks: The Drunkard's Path
Probability
L706
Brownian Motion: The Continuous Random Walk
Probability
L707
The Multinomial Distribution: Beyond Binary Outcomes
Probability
L716
The Exponential Distribution: Time Between Events
Probability
L717
The Gamma Distribution: Sum of Exponentials
Probability
L718
The Beta Distribution: Probability of Probabilities
Probability
L719
Conjugate Priors: When Bayesian Updates Stay in the Family
Probability
L720
The Central Limit Theorem: Formal Statement
Probability
L727
Covariance and the Covariance Matrix
Statistics
L728
The Multivariate Normal Distribution
Statistics
L729
Kolmogorov's Strong Law: Almost Sure Convergence
Probability
L732
The Glivenko-Cantelli Theorem: Empirical CDF Converges
Probability
L733
Order Statistics: The Mathematics of Ranking
Statistics
L738
Extreme Value Theory: Modeling the Worst Case
Statistics
L739
The Negative Binomial Distribution: Overdispersed Counts
Probability
L747
TERRITORY XVIII
The Laws of Chance
1850 CE - 1930 CE
0 / 25 LESSONS0%
Builds on XVII · New Machinery
Andrey Markov: Chains of Dependence
Lesson 673
Markov Chains: Memoryless Random Walks
Lesson 674
Markov Chains in Practice: From Text to Finance
Lesson 675
Pafnuty Chebyshev: Bounding Probability Without Distributions
Lesson 676
Chebyshev's Inequality: The Universal Bound
Lesson 677
Andrey Kolmogorov: Making Probability Rigorous
Lesson 679
Kolmogorov's Axioms: The Rules of Probability
Lesson 680
Edgeworth: The Generalized Central Limit Theorem
Lesson 686
Andrey Lyapunov: Stability and the CLT
Lesson 696
Emile Borel: Measure Theory and Probability
Lesson 697
Random Walks: The Drunkard's Path
Lesson 706
Brownian Motion: The Continuous Random Walk
Lesson 707
The Multinomial Distribution: Beyond Binary Outcomes
Lesson 716
The Exponential Distribution: Time Between Events
Lesson 717
The Gamma Distribution: Sum of Exponentials
Lesson 718
The Beta Distribution: Probability of Probabilities
Lesson 719
Conjugate Priors: When Bayesian Updates Stay in the Family
Lesson 720
The Central Limit Theorem: Formal Statement
Lesson 727
Covariance and the Covariance Matrix
Lesson 728
The Multivariate Normal Distribution
Lesson 729
Kolmogorov's Strong Law: Almost Sure Convergence
Lesson 732
The Glivenko-Cantelli Theorem: Empirical CDF Converges
Lesson 733
Order Statistics: The Mathematics of Ranking
Lesson 738
Extreme Value Theory: Modeling the Worst Case
Lesson 739
The Negative Binomial Distribution: Overdispersed Counts