Course - Probability

Created: October 17, 2022 | Updated: October 21, 2025 | Read markdown | About these notes | View in context | Study these flashcards

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An introduction to probability theory, starting from the axioms of a probability space and ending at the weak law of large numbers and Chebyshev’s inequality. A lot more than was covered in Stats at A-Level.

There were some really fun problem sheet questions in this course, like this one from Sheet 1: “Celia the centipede has 100 feet, 100 socks, and 100 shoes. How many orders can she choose from to put on her socks and shoes? (She must put a sock on foot $i$ before putting a shoe on foot $i$.)”.

• Course Webpage
• Lecture Notes
• Some of the lectures from this course are available on YouTube.
• Other courses this term: Courses MT22^U

Notes

• Notes - Probability MT22, Axioms of probability space^U
• Notes - Probability MT22, Basic definitions^U
• Notes - Probability MT22, Partition theorem^U
• Notes - Probability MT22, Bayes’ theorem^U
• Notes - Probability MT22, Random variables^U
• Notes - Probability MT22, Distributions^U
• Notes - Probability MT22, Expectations^U
• Notes - Probability MT22, Variance and covariance^U
• Notes - Probability MT22, Recurrence relations^U
• Notes - Probability MT22, Probability generating functions^U
• Notes - Probability MT22, Random sums theorem^U
• Notes - Probability MT22, Moments^U
• Notes - Probability MT22, Branching processes^U
• Notes - Probability MT22, Random samples^U
• Notes - Probability MT22, Weak law of large numbers^U
• Notes - Probability MT22, Markov’s inequality^U
• Notes - Probability MT22, Chebyshev’s inequality^U
• Notes - Probability MT22, Misc^U

Lectures

• Lecture - Probability, Lecture 1^U
• Lecture - Probability, Lecture 2^U
• Lecture - Probability, Lecture 3^U
• Lecture - Probability MT22, IV^U
• Lecture - Probability MT22, V^U
• Lecture - Probability MT22, VI^U
• Lecture - Probability MT22, VII^U
• Lecture - Probability MT22, VIII^U
• Lecture - Probability MT22, IX^U
• Lecture - Probability, X^U
• Lecture - Probability MT22, XI^U
• Lecture - Probability MT22, XII^U
• Lecture - Probability, XIII^U
• Lecture - Probability, XIV^U
• Lecture - Probability, XV^U
• Lecture - Probability, XVI^U

Problem Sheets

• Sheet 1
• Sheet 2
• Sheet 3
• Sheet 4
• Sheet 5
• Sheet 6
• Sheet 7
• Sheet 8

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