Transcription of Probability and Statistics Basics
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Probability and Statistics Basics
Probability and Statistics BasicsKevin Kircher Cornell MAE Spring 14 These notes summarize some basic Probability and Statistics material. The primarysources areA Modern Introduction to Probability and Statisticsby Dekking, Kraaikamp,Lopuha a and Meester,Introduction to Probabilityby Dimitri Bertsekas, and the lectures ofProfs. Gennady Samorodnitsky and Mark Probability31 Outcomes, Events and Probability32 Conditional Probability and Independence53 Discrete Random Variables74 Continuous Random Variables105 The Normal Distribution136 Expectation and Variance177 Joint Distributions and Independence198 Covariance and Correlation229 Random Vectors2410 Transformations of Random Variables2611 The Law of Large Numbers2912 Moment Generating Functions3113 Conditional Distributions32114 Order Statistics3515 The Central Limit Theorem3716 Stochastic Processes39II Statistics4217 Numerical Data Summa
Expectation: EX= p. Variance: Var(X) = p(1 p). Bernoulli trials form the basis of all the most important discrete RVs. The Bernoulli distribution models a sequence of independent binary trials (coin ips), with probability pof success in each trial. Xhas the binomial distribution Bin(n;p) with parameters n= 1;2;::: and 0 p 1 if its pmf is given ...
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