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Grinstead and Snell’s Introduction to Probability

GrinsteadandSnell'sIntroductionto ProbabilityTheCHANCEP roject1 Versiondated4 July20061 Copyright (C) a versionof GrinsteadandSnell's`Introductionto Probability , 2ndedition',publishedby theAmericanMathematicalSo-ciety, Copyright (C) freelyredistributableunderthetermsof ourwivesandin DiscreteProbability DiscreteProbabilities.. Distributions..182 ContinuousProbability ContinuousProbabilities.. Functions..553 .. ing.. 1204 .. 1755 Distributions.. Densities.. 2056 .. DiscreteRandomVariables.. 2687 Sumsof DiscreteRandomVariables.. ContinuousRandomVariables.. 2918 Law of .. 316vviCONTENTS9 .. Trials.. Trials.. 35610 .. 39311 Markov .. Chains.. Chains.. 45212 EuclideanSpace.. 'sRuin.. 493 Appendices499 Index503 PrefaceProbability theorybeganin seventeenth centuryFrancewhenthetwo greatFrenchmathematicians,BlaisePascalan dPierredeFermat,correspondedover two prob-lemsfromgamesof thosePascalandFermatsolved continuedto in uencesuch earlyresearchersas Huygens,Bernoulli,andDeMoivrein estab-lishinga mathematicaltheoryof Probability .

be e ective 30 percent of the time it is used, we might assign a probability .3 that the drug is e ective the next time it is used and .7 that it is not e ective. This last example illustrates the intuitive frequency concept of probability. That is, if we have a probability p that an experiment will result in outcome A, then if we repeat this

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