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A First Course in Probability

A First Course in Probability


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About the Book

The advancement of science in the twentieth century is marked by a special feature -- its transition from deterministic phenomena to probabilistic phenomena. For this reason the probability theory is introduced at the earliest possible level of any academic pursuit.

Written at an introductory level, A First Course in Probability takes an intuitive approach to proving the ethereal existence of probability, developing the subject step-by-step to show the accessibility of probability theory. The authors provide hundreds of problems from almost all spheres of life to demonstrate how probability plays a decisive role. Numerous routine and simple examples are solved throughout the text to demonstrate various techniques of solving practical problems. The more difficult problems are solved at the end of each chapter under the heading, "Miscellaneous Examples," and these are useful in solving problems in different competitive examinations.

Easy to understand and up-to-date, the text incorporates all the fundamental results while bringing forth the latest results. Some topics that can be avoided in the first reading are star-marked in the text.

Table of Contents:
PROBABILITY
Introduction
Algebra of Sets
Properties of Functions
Matrix Algebra
Three Approaches
Conditional Probability and Independence of Events
Geometric Probability
UNIVARIATE DISTRIBUTION
Random Variable
Expectation, Variance and Moments
Moment Generating Function
Characteristic Function and Cumulants
Some Standard Discrete Distributions
Some Standard Continuous Distributions
Transformation of Variables
BIVARIATE DISTRIBUTIONS
Joint, Marginal and Conditional Distributions
Moments, Conditional Moments
Correlation and Regression
Transformation of Variables
Bivariate Normal Distribution
Bivariate Dirichlet Distribution
MULTIVARIATE DISTRIBUTIONS
Different Aspects of a Multivariate Distribution
X2, t and F-Distributions
Correlation and Regression
Some Standard Multivariate Distributions
Order Statistics
Some Notions of Dependence
Results on Symmetrization
LIMIT THEOREMS
Chebyshev's Inequality
Other Useful Inequalities
Convergence in Distribution
Convergence in Probability
The Laws of Large Numbers
Central Limit Theorems


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Product Details
  • ISBN-13: 9780849309434
  • Publisher: Taylor & Francis Inc
  • Publisher Imprint: CRC Press Inc
  • Height: 229 mm
  • No of Pages: 468
  • Returnable: N
  • Width: 152 mm
  • ISBN-10: 0849309433
  • Publisher Date: 30 Oct 2000
  • Binding: Hardback
  • Language: English
  • No of Pages: 468
  • Weight: 1098 gr


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