Transcription of Probability - University of Cambridge
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Probability - University of Cambridge
ProbabilityAbout these people have written excellent notes for introductorycourses in Probability . Mine draw freely on material prepared by others in present-ing this course to students at Cambridge . I wish to acknowledge especially GeoffreyGrimmett, Frank Kelly and Doug order I follow is a bit different to that listed in the Schedules. Most of the materialcan be found in the recommended books by Grimmett & Welsh, and Ross. Many of theexamples are classics and mandatory in any sensible introductory course on book by Grinstead & Snell is easy reading and I know students have enjoyed are also some very good Wikipedia articles on many of the topics we will these notes I attempt a Goldilocks path by being neither too detailed or too brief. Each lecture has a title and focuses upon just one or two ideas. My notes for each lecture are limited to 4 also include some entertaining, but nonexaminable topics, some of which are unusualfor a course at this level (such as random permutations, entropy, reflection principle,Benford and Zipf distributions, Erd os s probabilistic method, value at risk, eigenvaluesof random matrices, Kelly criterion, Chernoff bound).
Probability theory is useful in the biological, physical, actuarial, management and com-puter sciences, in economics, engineering, and operations research. It helps in modeling complex systems and in decision-making when there is uncertainty. It can be used to prove theorems in other mathematical elds (such as analysis, number theory, game
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