Probability and Random Processes

Detalles Bibliográficos
Autor principal: Krishnan, Venkatarama
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Newark : John Wiley & Sons, Incorporated, 2015.
Colección:New York Academy of Sciences Ser.
Temas:
Electronic books.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Intro
  • TITLE PAGE
  • TABLE OF CONTENTS
  • PREFACE FOR THE SECOND EDITION
  • PREFACE FOR THE FIRST EDITION
  • 1 SETS, FIELDS, AND EVENTS
  • 1.1 SET DEFINITIONS
  • 1.2 SET OPERATIONS
  • 1.3 SET ALGEBRAS, FIELDS, AND EVENTS
  • 2 PROBABILITY SPACE AND AXIOMS
  • 2.1 PROBABILITY SPACE
  • 2.2 CONDITIONAL PROBABILITY
  • 2.3 INDEPENDENCE
  • 2.4 TOTAL PROBABILITY AND BAYES' THEOREM
  • 3 BASIC COMBINATORICS
  • 3.1 BASIC COUNTING PRINCIPLES
  • 3.2 PERMUTATIONS
  • 3.3 COMBINATIONS
  • 4 DISCRETE DISTRIBUTIONS
  • 4.1 BERNOULLI TRIALS
  • 4.2 BINOMIAL DISTRIBUTION
  • 4.3 MULTINOMIAL DISTRIBUTION
  • 4.4 GEOMETRIC DISTRIBUTION
  • 4.5 NEGATIVE BINOMIAL DISTRIBUTION
  • 4.6 HYPERGEOMETRIC DISTRIBUTION
  • 4.7 POISSON DISTRIBUTION
  • 4.8 NEWTON-PEPYS PROBLEM AND ITS EXTENSIONS
  • 4.9 LOGARITHMIC DISTRIBUTION
  • 4.10 SUMMARY OF DISCRETE DISTRIBUTIONS
  • 5 RANDOM VARIABLES
  • 5.1 DEFINITION OF RANDOM VARIABLES
  • 5.2 DETERMINATION OF DISTRIBUTION AND DENSITY FUNCTIONS
  • 5.3 PROPERTIES OF DISTRIBUTION AND DENSITY FUNCTIONS
  • 5.4 DISTRIBUTION FUNCTIONS FROM DENSITY FUNCTIONS
  • 6 CONTINUOUS RANDOM VARIABLES AND BASIC DISTRIBUTIONS
  • 6.1 INTRODUCTION
  • 6.2 UNIFORM DISTRIBUTION
  • 6.3 EXPONENTIAL DISTRIBUTION
  • 6.4 NORMAL OR GAUSSIAN DISTRIBUTION
  • 7 OTHER CONTINUOUS DISTRIBUTIONS
  • 7.1 INTRODUCTION
  • 7.2 TRIANGULAR DISTRIBUTION
  • 7.3 LAPLACE DISTRIBUTION
  • 7.4 ERLANG DISTRIBUTION
  • 7.5 GAMMA DISTRIBUTION
  • 7.6 WEIBULL DISTRIBUTION
  • 7.7 CHI-SQUARE DISTRIBUTION
  • 7.8 CHI AND OTHER ALLIED DISTRIBUTIONS
  • 7.9 STUDENT-t DENSITY
  • 7.10 SNEDECOR F DISTRIBUTION
  • 7.11 LOGNORMAL DISTRIBUTION
  • 7.12 BETA DISTRIBUTION
  • 7.13 CAUCHY DISTRIBUTION
  • 7.14 PARETO DISTRIBUTION
  • 7.15 GIBBS DISTRIBUTION
  • 7.16 MIXED DISTRIBUTIONS
  • 7.17 SUMMARY OF DISTRIBUTIONS OF CONTINUOUS RANDOM VARIABLES
  • 8 CONDITIONAL DENSITIES AND DISTRIBUTIONS
  • 8.1 CONDITIONAL DISTRIBUTION AND DENSITY FOR P{A}
  • 8.2 CONDITIONAL DISTRIBUTION AND DENSITY FOR P{A} = 0
  • 8.3 TOTAL PROBABILITY AND BAYES' THEOREM FOR DENSITIES
  • 9 JOINT DENSITIES AND DISTRIBUTIONS
  • 9.1 JOINT DISCRETE DISTRIBUTION FUNCTIONS
  • 9.2 JOINT CONTINUOUS DISTRIBUTION FUNCTIONS
  • 9.3 BIVARIATE GAUSSIAN DISTRIBUTIONS
  • 10 MOMENTS AND CONDITIONAL MOMENTS
  • 10.1 EXPECTATIONS
  • 10.2 VARIANCE
  • 10.3 MEANS AND VARIANCES OF SOME DISTRIBUTIONS
  • 10.4 HIGHER-ORDER MOMENTS
  • 10.5 CORRELATION AND PARTIAL CORRELATION COEFFICIENTS
  • 11 CHARACTERISTIC FUNCTIONS AND GENERATING FUNCTIONS
  • 11.1 CHARACTERISTIC FUNCTIONS
  • 11.2 EXAMPLES OF CHARACTERISTIC FUNCTIONS
  • 11.3 GENERATING FUNCTIONS
  • 11.4 EXAMPLES OF GENERATING FUNCTIONS
  • 11.5 MOMENT GENERATING FUNCTIONS
  • 11.6 CUMULANT GENERATING FUNCTIONS
  • 11.7 TABLE OF MEANS AND VARIANCES
  • 12 FUNCTIONS OF A SINGLE RANDOM VARIABLE
  • 12.1 RANDOM VARIABLE g(X)
  • 12.2 DISTRIBUTION OF Y = g(X)
  • 12.3 DIRECT DETERMINATION OF DENSITY fY(y) from fX(x)
  • 12.4 INVERSE PROBLEM: FINDING g(x) GIVEN fX(x) AND fY(y)

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