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Abstract/Sommario: The nature of probability theory - The sample space - Elements of combinatorial analysis. Stirling's formula - The simplest occupancy and ordering problems - Combination of events - Conditional probability. Statistical independence - The binomial and the Poisson distributions - The normal approximation to the binomial distribution - Unlimited sequences of Bernoulli trials - Random variables; expectation - Laws of large numbers - Integral valued variables. Generating functions - Recurre ...; [Leggi tutto...] The nature of probability theory - The sample space - Elements of combinatorial analysis. Stirling's formula - The simplest occupancy and ordering problems - Combination of events - Conditional probability. Statistical independence - The binomial and the Poisson distributions - The normal approximation to the binomial distribution - Unlimited sequences of Bernoulli trials - Random variables; expectation - Laws of large numbers - Integral valued variables. Generating functions - Recurrent events: theory - Recurrent events: applications to runs and renewal theory - Random walk and ruin problems - Markov chains - Algebraic treatment of finite Markov chains - The simplest time-dependent stochastic processes.

Abstract/Sommario: Scientific method-truth; mathematics and logic-validity; outlines of some useful mathematical models - Optimization, programming, and game theory - Probability, applications, statistics, and queueing theory - An essay - Index.

Abstract/Sommario: Introduction - Probability - Sampling - Inventory - Replacement - Waiting lines - Competitive strategies - Allocation - Sequencing - Dynamic programming - Appendices.

Abstract/Sommario: The general decision problem - The probability background - Uniformly most powerful tests - Unbiasedness: theory and first applications - Unbiasedness: applications to normal distributions; confidence intervals - Invariance - Linear hypotheses - The minimax principle - Appendix.

Abstract/Sommario: Definition of information - Properties of information - Inequalities of information theory - Limiting properties - Information statistics - Multinomial populations - Poisson populations - Contingency tables - Multivariate normal populations - The linear hypothesis - Multivariate analysis; the multivariate linear hypothesis - Multivariate analysis: other hypothesis - Linear discriminant functions - References.

Abstract/Sommario: Methods based on the representation of the solution as an infinite series - The approximate solution of the integral equations of Fredholm - The method of nets - Variational methods - The conformal transformation of regions - Principles of the application of conformal transformation to the solution of the fundamental problems for canonical regions - Schwarz's method.

Abstract/Sommario: Equilibrium systems and comparative statistics - The theory of maximizing behavior - A comprehensive restatement of the theory of cost and production - The pure theory of consumer's behavior - Transformations, composite commodities, and rationing - Some special aspects of the theory of consumer's behavior - Welfare economics - The stability of equilibrium: comparative statics and dynamics - The stability of equilibrium: linear and non-linear systems - Some fundamentals of dynamical the ...; [Leggi tutto...] Equilibrium systems and comparative statistics - The theory of maximizing behavior - A comprehensive restatement of the theory of cost and production - The pure theory of consumer's behavior - Transformations, composite commodities, and rationing - Some special aspects of the theory of consumer's behavior - Welfare economics - The stability of equilibrium: comparative statics and dynamics - The stability of equilibrium: linear and non-linear systems - Some fundamentals of dynamical theory - Conclusion.

Abstract/Sommario: Introduction - Topological spaces - Particular types of topological spaces - Homotopy - Simplicial complexes - Homology.

Abstract/Sommario: Estimation: likelihood - Estimation: miscellaneous methods - Confidence intervals - Fiducial inference - Some common tests of significance - Regression - The analysis of variance - The design of sampling inquiries - General theory of significance tests - Multivariate analysis - Time series - Appendices.

Abstract/Sommario: The integers - Rational numbers and fields - Polynomials - Real numbers - Complex numbers - Group theory - Vectors and vector spaces - The algebra of matrices - Linear groups - Determinants and canonical forms - Algebra of classes - Transfinite arithmetic - Rings and ideals - Algebraic number fields - Galois theory.