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Browse materialsMIT 18.175 · Spring 2014

Theory of Probability

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Instructor: Prof. Scott Sheffield
Term: Spring 2014
Level: Graduate
What's inside: 3 problem sets · 1 reading · 38 other files · 4 web pages
Materials open: MIT OCW

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About this course

Source: MIT OpenCourseWare 18.175 Theory of Probability, Spring 2014, Prof. Scott Sheffield — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: MIT's own listing order, section by section. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 23, 2026. How RedLectern is built.

Materials are grouped the way MIT organized them. A verified, course-wide order has not been established here.

Before you start

Prerequisites are not listed here. Check MIT's own syllabus for this course.

This course’s cited books, in our reading lists: Probability: Theory and Examples

How this course was organized

What's here, and what isn't

MIT's own materials here did not support a verified, course-wide order, so they are grouped by section instead.

Not included here

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Materials by section

Grouped by section, as MIT organized them. Not sequenced or ordered.

Lecture Slides

35 files

Assignments

Other materials from this course

MIT OpenCourseWare, Prof. Scott Sheffield, 18.175 Theory of Probability, Spring 2014.

License: CC BY-NC-SA 4.0 · Edition: Spring 2014 · Open the original course on OCW ↗

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Theory of Probability

Before you start

What's here, and what isn't

Not included here

Materials by section

Lecture Slides

Assignments

Other materials from this course

Lecture 1: Probability Spaces and Sigma-Algebras

Lecture 2: Extension Theorems: A Tool for Constructing Measures

Lecture 3: Random Variables and Distributions

Lecture 4: Integration

Lecture 5: More Integration and Expectation

Lecture 6: Laws of Large Numbers and Independence

Lecture 7: Sums of Random Variables

Lecture 8: Weak Laws and Moment-Generating and Characteristic Functions

Lecture 9: Borel-Cantelli and the Strong Law of Large Numbers

Lecture 10: Zero-One Laws and Maximal Inequalities

Lecture 11: Independent Sums and Large Deviations

Lecture 12: DeMoivre-Laplace and Weak Convergence

Lecture 13: Large Deviations

Lecture 14: Weak Convergence and Characteristic Functions

Lecture 15: Characteristic Functions and Central Limit Theorem

Lecture 16: Central Limit Theorem Variants

Lecture 17: Poisson Random Variables

Lecture 18: Stable Random Variables

Lecture 19: Higher Dimensional Limit Theorems

Lecture 20: Infinite Divisibility and Levy Processes

Lecture 21: More on Infinite Divisibility and Levy Processes

Lecture 22: More on Infinite Divisibility and Levy Processes

Lecture 23: Random Walks

Lecture 24: More on Random Walks

Lecture 25: Reflections and Martingales

Lecture 26: More on Martingales

Lecture 27: More on Martingales (cont.)

Lecture 28: Even More on Martingales

Lecture 29: Still More Martingales

Lecture 30: Markov Chains

Lecture 31: More Markov Chains

Lecture 32: Additional Material on Markov Chains

Lecture 33: Ergodic Theory

Lecture 34: More Ergodic Theory

Lecture 35: Ergodic Theory

Lecture 36: Brownian Motion

Lecture 37: More Brownian Motion

Lecture 38: Even More Brownian Motion

Lecture 39: Last Lecture