Fundamentals of Probability / Edition 2

Fundamentals of Probability / Edition 2

by Saeed Ghahramani
     
 

ISBN-10: 0130113298

ISBN-13: 9780130113290

Pub. Date: 09/02/1999

Publisher: Prentice Hall

This book is a valuable reference to Basic Probability and related problems, featuring unique discussions published in recent journals to support individual investigation. Chapter topics include combinatorial methods, conditional probability and independence, random variables, distributions, and simulation. For professionals in the fields of computer and actuarial

Overview

This book is a valuable reference to Basic Probability and related problems, featuring unique discussions published in recent journals to support individual investigation. Chapter topics include combinatorial methods, conditional probability and independence, random variables, distributions, and simulation. For professionals in the fields of computer and actuarial science, electrical and industrial engineering,, operations research, applied mathematics, and statistics, who desire additional input to help solve the indeterministic business, government, and engineering problems they encounter at work.

Product Details

ISBN-13:
9780130113290
Publisher:
Prentice Hall
Publication date:
09/02/1999
Edition description:
Older Edition
Pages:
511
Product dimensions:
6.14(w) x 9.30(h) x 1.11(d)

Related Subjects

Table of Contents

Prefacexi
1Axioms of Probability1
1.1Introduction1
1.2Sample Space and Events4
1.3Axioms of Probability11
1.4Basic Theorems18
1.5Continuity of Probability Function27
1.6Probabilities 0 and 129
1.7Random Selection of Points from Intervals31
Review Problems35
2Combinatorial Methods38
2.1Introduction38
2.2Counting Principle38
Number of Subsets of a Set42
Tree Diagrams43
2.3Permutations47
2.4Combinations54
2.5Stirling's Formula70
Review Problems72
3Conditional Probability and Independence75
3.1Conditional Probability75
Reduction of Sample Space79
3.2Law of Multiplication85
3.3Law of Total Probability89
3.4Bayes' Formula99
3.5Independence106
Review Problems126
4Distribution Functions and Discrete Random Variables129
4.1Random Variables129
4.2Distribution Functions134
4.3Discrete Random Variables143
4.4Expectations of Discrete Random Variables150
4.5Variances and Moments of Discrete Random Variables161
Moments167
4.6Standardized Random Variables170
Review Problems171
5Special Discrete Distributions174
5.1Bernoulli and Binomial Random Variables174
Expectations and Variances of Binomial Random Variables180
5.2Poisson Random Variable188
Poisson as an Approximation to Binomial188
Poisson Process194
5.3Other Discrete Random Variables203
Geometric Random Variable203
Negative Binomial Random Variable205
Hypergeometric Random Variable207
Review Problems215
6Continuous Random Variables218
6.1Probability Density Functions218
6.2Density Function of a Function of a Random Variable227
6.3Expectations and Variances233
Expectations of Continuous Random Variables233
Variances of Continuous Random Variables239
Review Problems245
7Special Continuous Distributions247
7.1Uniform Random Variable247
7.2Normal Random Variable254
Correction for Continuity257
7.3Exponential Random Variable269
7.4Gamma Distribution276
7.5Beta Distribution281
Review Problems285
8Joint distributions287
8.1Bivariate Distributions287
Joint Probability Functions287
Joint Probability Density Functions290
8.2Independent Random Variables305
8.3Conditional Distributions316
8.4Multivariate Distributions329
8.5Order Statistics345
8.6Multinomial Distributions352
8.7Transformations of Two Random Variables356
Review Problems362
9More Expectations and Variances367
9.1Expected Values of Sums of Random Variables367
Pattern Appearance376
9.2Covariance383
9.3Correlation392
9.4Conditioning on Random Variables397
9.5Bivariate Normal Distribution408
Review Problems414
10Sums of Independent Random Variables and Limit Theorems416
10.1Moment-Generating Functions416
10.2Sums of Independent Random Variables427
10.3Markov and Chebyshev Inequalities437
10.4Laws of Large Numbers443
10.5Central Limit Theorem452
Review Problems458
11Simulation461
11.1Introduction461
11.2Simulation of Combinatorial Problems466
11.3Simulation of Conditional Probabilities469
11.4Simulation of Random Variables473
11.5Monte Carlo Method481
Appendix Tables487
Answers to Odd-Numbered Exercises491
Index501

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