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

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Problems in Probability Theory, Mathematical Statistics and Theory of Random Fun Cover

 

Synopses & Reviews

Synopsis:

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.

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

Product Details

ISBN:
9780486637174
Translator:
Silverman, Richard A.
Author:
Silverman, Richard A.
Author:
Sveshnikov, A. A.
Author:
Mathematics
Publisher:
Dover Publications
Location:
New York :
Subject:
General
Subject:
Mathematics
Subject:
Statistics
Subject:
Mathematical statistics
Subject:
Probability
Subject:
Probabilities
Subject:
Stochastic processes
Subject:
Mathematical statistics -- Problems, exercises, etc.
Subject:
Probability & Statistics - General
Subject:
General Mathematics
Subject:
Probabilities -- Problems, exercises, etc.
Subject:
Mathematics | Probability and Statistics
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Series Volume:
no. 80, 84
Publication Date:
19790231
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
512
Dimensions:
9.25 x 6.13 in 1.88 lb

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Problems in Probability Theory, Mathematical Statistics and Theory of Random Fun New Trade Paper
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Product details 512 pages Dover Publications - English 9780486637174 Reviews:
"Synopsis" by ,
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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