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Problems in Probability Theory, Mathematical Statistics and Theory of Random Functions

Overview

Approximately 1,000 problems ? with answers and solutions included at the back of the book ? illustrate such topics as random events, random variables, limit theorems, Markov processes, and much more.

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Problems in Probability Theory, Mathematical Statistics and Theory of Random Functions

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Overview

Approximately 1,000 problems — with answers and solutions included at the back of the book — illustrate such topics as random events, random variables, limit theorems, Markov processes, and much more.

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Product Details

  • ISBN-13: 9780486637174
  • Publisher: Dover Publications
  • Publication date: 2/1/1979
  • Series: Dover Books on Mathematics Series
  • Pages: 481
  • Product dimensions: 6.13 (w) x 9.19 (h) x 0.94 (d)

Table of Contents

I. RANDOM EVENTS
  1. Relations among random events
  2. A direct method for evaluating probabilities
  3. Geometric probabilities
  4. Conditonal probability. The multiplication theorem for probabilities
  5. The addition theorem for probabilities
  6. The total probability formula
  7. Computation of the probabilities of hypotheses after a trial (Bayes' formula)
  8. Evaluation of probabilities of occurrence of an event in repeated independent trials
  9. The multinomial distribution. Recursion formulas. Generating functions
II. RANDOM VARIABLES
  10. "The probability distribution series, the distribution polygon and the distribution function of a discrete random variable"
  11. The distribution function and the probability density function of a continuous random variable
  12. Numerical characteristics of discrete random variables
  13. Numerical characteristics of continuous random variables
  14. Poisson's law
  15. The normal distribution law
  16. Characteristic functions
  17. The computation of the total probability and the probability density in terms of conditional probability
III. SYSTEMS OF RANDOM VARIABLES
  18. Distribution laws and numerical characteristics of systems of random variables
  19. The normal distribution law in the plane and in space. The multidimensional normal distribution
  20. Distribution laws of subsystems of continuous random variables and conditional distribution laws
IV. NUMERICAL CHARACTERISTICS AND DISTRIBUTION LAWS OF FUNCTIONS OF RANDOM VARIABLES
  21. Numerical characteristics of functions of random variables
  22. The distribution laws of functions of random variables
  23. The characteristic functions of systems and functions of random variables
  24. Convolution of distribution laws
  25. The linearization of functions of random variables
  26. The convolution of two-dimensional and three-dimensional normal distribution laws by use of the notion of deviation vectors
V. ENTROPY AND INFORMATION
  27. The entropy of random events and variables
  28. The quantity of information
VI. THE LIMIT THEOREMS
  29. The law of large numbers
  30. The de Moivre-Laplace and Lyapunov theorems
VII. THE CORRELATION THEORY OF RANDOM FUNCTIONS
  31. General properties of correlation functions and distribution laws of random functions
  32. Linear operations with random functions
  33. Problems on passages
  34. Spectral decomposition of stationary random functions
  35. Computation of probability characteristics of random functions at the output of dynamical systems
  36. Optimal dynamical systems
  37. The method of envelopes
VIII. MARKOV PROCESSES
  38. Markov chains
  39. The Markov processes with a discrete number of states
  40. Continuous Markov processes
IX. METHODS OF DATA PROCESSNG
  41. Determination of the moments of random variables from experimental data
  42. Confidence levels and confidence intervals
  43. Tests of goodness-of-fit
  44. Data processing by the method of least squares
  45. Statistical methods of quality control
  46. Determination of probability characteristics of random functions from experimental data
  ANSWERS AND SOLUTIONS
  SOURCES OF TABLES REFERRED TO IN THE TEXT
  BIBLIOGRAPHY
  INDEX
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