Author | Nguyen, Hung T. author |
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Title | Fundamentals of Mathematical Statistics [electronic resource] : Probability for Statistics / by Hung T. Nguyen, Gerald S. Rogers |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1989 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-1013-9 |
Descript | X, 432 p. online resource |
I:Elementary Probability and Statistics -- 1 Relative frequency -- 2 Sample spaces -- * 3 Some rules about sets (see footnote) -- 4 The counting function for finite sets -- 5 Probability on finite sample spaces -- * 6 Ordered selections -- * 7 Unordered selections -- 8 Some uniform probability spaces -- 9 Conditional probability/independence -- * 10 Bayesโ rule -- 11 Random variables -- 12 Expectation -- 13 A hypergeometric distribution -- * 14 Sampling and simulation -- 15 Testing simple hypotheses -- * 16 An acceptance sampling plan -- 17 The binomial distribution -- * 18 Matching and catching -- 19 Confidence intervals for a Bernoulli ? -- 20 The Poisson distribution -- * 21 The negative binomial distribution -- II:Probability and Expectation -- 1 Some set theory -- 2 Basic probability theory -- 3 The cumulative distribution function -- 4 Some continuous CDFs -- 5 The normal distribution -- 6 Some algebra of random variables -- 7 Convergence of sequences of random variables -- 8 Convergence almost surely and in probability -- 9 Integration-I -- * 10 Integration-II -- 11 Theorems for expectation -- 12 Stieltjes integrals -- 13 Product measures and integrals -- III:Limiting Distributions -- 1 Joint distributions: discrete -- 2 Conditional distributions: discrete -- 3 Joint distributions: continuous -- 4 Conditional distributions: continuous -- 5 Expectation: examples -- 6 Convergence in mean, in distribution -- * 7 Other relations in modes of convergence -- 8 Laws of large numbers -- 9 Convergence of sequences of distribution functions -- 10 Convergence of sequences of integrals -- 11 On the sum of random variables -- 12 Characteristic functions-I -- 13 Characteristic functions-II -- 14 Convergence of sequences of characteristic functions -- 15 Central limit theorems -- References