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ProbabilityTheory - Harvard Mathematics Department

probability TheoryCourse Notes Harvard University 2011C. McMullenSeptember 28, 2017 ContentsI The Sample Space .. 2II Elements of Combinatorial Analysis .. 5 III Random Walks .. 15IV Combinations of Events .. 24V Conditional probability .. 29VI The Binomial and Poisson Distributions .. 37 VII Normal Approximation .. 44 VIII Unlimited Sequences of Bernoulli Trials ..55IX Random Variables and Expectation .. 60X Law of Large Numbers .. 68XI Integral Valued Variables. Generating Functions .. 70 XIV Random Walk and Ruin Problems .. 70I The Exponential and the Uniform Density.

These course notes accompany Feller, An Introduction to Probability Theory and Its Applications, Wiley, 1950. I TheSample Space Some sources and uses of randomness, and philosophical conundrums.

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