Description: 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 Bayes' 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.

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