Probability and Mathematical Statistics
Random events and the basic concepts of probability; Axiomatic formulation of the theory of probability; Probabilitices in a finite sample space: Elements of combinatorial algebra; Random variables and probability distritions; Expected valores and moments; Distributions involving a discrete random variable; Special continuous distributions; Random variables; Covolutin; Multivariante nomal distrbution; Sistributions associated with the normal;Samopling from general populations; Point estimation; Maximun likelihood estimation;Hypothesis testing; Interval estimation; The linear regression model and the principle of least squares; Order statistics; Statistical imference in perspective; Appendix 1 the algebra of the subsets of a set; Appendix 2 Binomial and multino-mial theoremas; Appendix 3 Characteristic functions and related theorems; greens theorem and other results from advanced calculus; Appendix 5 Real symmetric;Positive definite; And idempatent matrices; Appendix 6 the lindeberg-levy central limit theorem.
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Axiomatic Formulation of the Theory of Probability
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Accordingly assume assumption becomes begin binomial called chap chapter Consequently consider consistent continuous covariance defined definition denote density function depend derive determined discrete discussion drawn at random elements equal Equation error estimator evident example exists expected expression fact Figure Finally finite follows formula frequency function f(x given Hence hypothesis implies independent inference integral interested interval joint density known least limit linear marginal matrix mean moment-generating function moments namely normal distribution noted objects observations obtained occur outcomes parameter particular population positive possible principle probability problem proof prove provides quantity question random variable referred region reject replacement respect result sample sample mean shows situations space squares sufficient statistic suppose Table theorem theory tion transformation trials true unbiased estimator usually variance zero