06-25-2026, 10:30 AM
Probability Theory Notes
by Amir Dembo
These Stanford probability theory notes by Amir Dembo provide a rigorous introduction to modern probability, building the subject from its mathematical foundations rather than focusing only on calculations. The notes begin with measure theory, probability spaces, random variables, and integration, then develop key concepts such as independence, conditional expectation, convergence of random variables, and important inequalities.
From there, they explore the major limit theorems that explain the behavior of randomness in large systems, including the Law of Large Numbers and the Central Limit Theorem. Throughout, the emphasis is on understanding why probabilistic results are true through precise proofs and mathematical reasoning. As a result, the notes serve as an advanced guide for students in mathematics, statistics, data science, and related fields who want a deep theoretical understanding of uncertainty and stochastic processes rather than just practical statistical methods.
BOOK
by Amir Dembo
These Stanford probability theory notes by Amir Dembo provide a rigorous introduction to modern probability, building the subject from its mathematical foundations rather than focusing only on calculations. The notes begin with measure theory, probability spaces, random variables, and integration, then develop key concepts such as independence, conditional expectation, convergence of random variables, and important inequalities.
From there, they explore the major limit theorems that explain the behavior of randomness in large systems, including the Law of Large Numbers and the Central Limit Theorem. Throughout, the emphasis is on understanding why probabilistic results are true through precise proofs and mathematical reasoning. As a result, the notes serve as an advanced guide for students in mathematics, statistics, data science, and related fields who want a deep theoretical understanding of uncertainty and stochastic processes rather than just practical statistical methods.
BOOK
┌────────────────────────────────┐
│ KONSTANTINOS MICHAILIDIS │
└────────────────────────────────┘
│ KONSTANTINOS MICHAILIDIS │
└────────────────────────────────┘