# Part I: The Fundamentals

The videos in Part I introduce the general framework of probability models, multiple discrete or continuous random variables, expectations, conditional distributions, and various powerful tools of general applicability.

The textbook for this subject is Bertsekas, Dimitri, and John Tsitsiklis. Introduction to Probability. 2nd ed. Athena Scientific, 2008. ISBN: 9781886529236.

The authors have made this Selected Summary Material (PDF) available for OCW users.

L = Lecture Content

S = Supplemental Content

SES # & TOPICS SLIDES
Lecture 1: Probability Models and Axioms

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Lecture 1 Slides (PDF - 1.5MB)

Lecture 1 Slides Annotated (PDF)

Lecture 1 Supplement: Mathematical Background

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Math Overview Slides (PDF)

Lecture 2: Conditioning and Bayes' Rule

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Lecture 2 Slides Annotated (PDF)

Lecture 3: Independence

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Lecture 3 Slides (PDF)

Lecture 3 Slides Annotated (PDF)

Lecture 4: Counting

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Lecture 4 Slides (PDF - 1.0MB)

Lecture 4 Slides Annotated (PDF)

Lecture 5: Discrete Random Variables Part I

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Lecture 5 Slides (PDF - 1.9MB)

Lecture 5 Slides Annotated (PDF - 1.1MB)

Lecture 6: Discrete Random Variables Part II

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Lecture 6 Slides Annotated (PDF - 1.1MB)

Lecture 7: Discrete Random Variables Part III

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Lecture 7 Slides (PDF - 1.1MB)

Lecture 7 Slides Annotated (PDF)

Lecture 8: Continuous Random Variables Part I

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Lecture 8 Slides Annotated (PDF - 1.2MB)

Lecture 9: Continuous Random Variables Part II

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Lecture 9 Slides (PDF - 1.7MB)

Lecture 9 Slides Annotated (PDF)

Lecture 10: Continuous Random Variables Part III

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Lecture 10 Slides Annotated (PDF)

Lecture 11: Derived Distributions

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Lecture 11 Slides (PDF)

Lecture 11 Slides Annotated (PDF)

Lecture 12: Sum of Independent R.V.s. Covariance and Correlation

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Lecture 12 Slides Annotated (PDF)

Lecture 13: Conditional Expectation & Variance Revisited; Sum of a Random Number of Independent R.V.s

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Lecture 13 Slides (PDF - 1.2MB)

Lecture 13 Slides Annotated (PDF)