Elsevier S & T

Fundamentals of Applied Probability and Random Processes

In stock
No reviews
47.750 KD inc. VAT
License
Table of contents
  • Contentsv
  • Prefacexiii
  • Acknowledgmentxvii
  • 1 Basic Probability Concepts1
  • Introduction1
  • Sample Space and Events2
  • Definitions of Probability4
  • Axiomatic Definition4
  • Relative-Frequency Definition5
  • Classical Definition5
  • Applications of Probability7
  • Reliability Engineering7
  • Quality Control7
  • Channel Noise7
  • System Simulation8
  • Elementary Set Theory8
  • Set Operations9
  • Number of Subsets of a Set10
  • Venn Diagram10
  • Set Identities10
  • Duality Principle13
  • Properties of Probability13
  • Conditional Probability15
  • Total Probability and the Bayes’ Theorem16
  • Tree Diagram24
  • Independent Events26
  • Combined Experiments29
  • Basic Combinatorial Analysis31
  • Permutations31
  • Circular Arrangement33
  • Applications of Permutations in Probability33
  • Combinations35
  • The Binomial Theorem37
  • Stirling’s Formula37
  • Applications of Combinations in Probability38
  • Reliability Applications42
  • Chapter Summary47
  • Problems47
  • References57
  • 2 Random Variables59
  • Introduction59
  • Definition of a Random Variable59
  • Events Defined by Random Variables61
  • Distribution Functions62
  • Discrete Random Variables63
  • Obtaining the PMF from the CDF68
  • Continuous Random Variables70
  • Chapter Summary75
  • Problems76
  • 3 Moments of Random Variables85
  • Introduction85
  • Expectation86
  • Expectation of Nonnegative Random Variables88
  • Moments of Random Variables and the Variance90
  • Conditional Expectations101
  • The Chebyshev Inequality102
  • The Markov Inequality103
  • Chapter Summary104
  • Problems104
  • 4 Special Probability Distributions111
  • Introduction111
  • The Bernoulli Trial and Bernoulli Distribution112
  • Binomial Distribution113
  • Geometric Distribution116
  • Modified Geometric Distribution119
  • ForgetfulnessŽ Property of the Geometric Distribution120
  • Pascal (or Negative Binomial) Distribution122
  • Hypergeometric Distribution126
  • Poisson Distribution130
  • Poisson Approximation to the Binomial Distribution132
  • Exponential Distribution133
  • ForgetfulnessŽ Property of the Exponential Distribution134
  • Relationship between the Exponential and Poisson Distributions136
  • Erlang Distribution136
  • Uniform Distribution141
  • The Discrete Uniform Distribution142
  • Normal Distribution144
  • Normal Approximation to the Binomial Distribution147
  • The Error Function149
  • The Q-Function150
  • The Hazard Function150
  • Chapter Summary153
  • Problems155
  • 5 Multiple Random Variables167
  • Introduction167
  • Joint CDFs of Bivariate Random Variables167
  • Properties of the Joint CDF168
  • Discrete Random Variables169
  • Continuous Random Variables173
  • Determining Probabilities from a Joint CDF175
  • Conditional Distributions178
  • Conditional PMF for Discrete Random Variables178
  • Conditional PDF for Continuous Random Variables179
  • Conditional Means and Variances180
  • Simple Rule for Independence182
  • Covariance and Correlation Coefficient184
  • Many Random Variables187
  • Multinomial Distributions189
  • Chapter Summary190
  • Problems190
  • 6 Functions of Random Variables197
  • Introduction197
  • Functions of One Random Variable198
  • Linear Functions198
  • Power Functions199
  • Expectation of a Function of One Random Variable201
  • Moments of a Linear Function201
  • Sums of Independent Random Variables202
  • Moments of the Sum of Random Variables209
  • Sum of Discrete Random Variables210
  • Sum of Independent Binomial Random Variables214
  • Sum of Independent Poisson Random Variables214
  • The Spare Parts Problem215
  • Minimum of Two Independent Random Variables218
  • Maximum of Two Independent Random Variables219
  • Comparison of the Interconnection Models221
  • Two Functions of Two Random Variables222
  • Application of the Transformation Method224
  • Laws of Large Numbers226
  • The Central Limit Theorem227
  • Order Statistics229
  • Chapter Summary233
  • Problems234
  • 7 Transform Methods241
  • Introduction241
  • The Characteristic Function242
  • Moment-Generating Property of the Characteristic Function243
  • The s-Transform245
  • Moment-Generating Property of the s-Transform245
  • The s-Transforms of Some Well-Known PDFs246
  • The s-Transform of the PDF of the Sum of Independent Random Variables247
  • The z-Transform250
  • Moment-Generating Property of the z-Transform252
  • The z-Transform of the Bernoulli Distribution253
  • The z-Transform of the Binomial Distribution254
  • The z-Transform of the Geometric Distribution254
  • The z-Transform of the Poisson Distribution255
  • The z-Transform of the PMF of the Sum of Independent Random Variables255
  • The z-Transform of the Pascal Distribution256
  • Random Sum of Random Variables256
  • Chapter Summary261
  • Problems261
  • 8 Introduction to Random Processes267
  • Introduction267
  • Classification of Random Processes269
  • Characterizing a Random Process269
  • Mean and Autocorrelation Function of a Random Process270
  • The Autocovariance Function of a Random Process271
  • Crosscorrelation and Crosscovariance Functions272
  • Review of Some Trigonometric Identities273
  • Stationary Random Processes275
  • Strict-Sense Stationary Processes275
  • Wide-Sense Stationary Processes275
  • Ergodic Random Processes282
  • Power Spectral Density284
  • White Noise289
  • Discrete-Time Random Processes290
  • Mean, Autocorrelation Function, and Autocovariance Function290
  • Power Spectral Density291
  • Sampling of Continuous-Time Processes292
  • Chapter Summary293
  • Problems294
  • 9 Linear Systems with Random Inputs305
  • Introduction305
  • Overview of Linear Systems with Deterministic Inputs305
  • Linear Systems with Continuous-Time Random Inputs307
  • Linear Systems with Discrete-Time Random Inputs313
  • Autoregressive Moving Average Process316
  • Moving Average Process316
  • Autoregressive Process319
  • ARMA Process322
  • Chapter Summary323
  • Problems323
  • 10 Some Models of Random Processes333
  • Introduction333
  • The Bernoulli Process333
  • Random Walk335
  • Gambler’s Ruin337
  • The Gaussian Process339
  • White Gaussian Noise Process341
  • Poisson Process342
  • Counting Processes342
  • Independent Increment Processes343
  • Stationary Increments343
  • Definitions of a Poisson Process344
  • Interarrival Times for the Poisson Process345
  • Conditional and Joint PMFs for Poisson Processes346
  • Compound Poisson Process347
  • Combinations of Independent Poisson Processes349
  • Competing Independent Poisson Processes350
  • Subdivision of a Poisson Process and the Filtered Poisson Process352
  • Random Incidence353
  • Nonhomogeneous Poisson Process356
  • Markov Processes358
  • Discrete-Time Markov Chains359
  • State Transition Probability Matrix360
  • The n-Step State Transition Probability360
  • State Transition Diagrams361
  • Classification of States363
  • Limiting-State Probabilities366
  • Doubly Stochastic Matrix369
  • Continuous-Time Markov Chains370
  • Birth and Death Processes373
  • Gambler's Ruin as a Markov Chain376
  • Chapter Summary378
  • Problems378
  • 11 Introduction to Statistics395
  • Introduction395
  • Sampling Theory396
  • The Sample Mean397
  • The Sample Variance399
  • Sampling Distributions400
  • Estimation Theory402
  • Point Estimate, Interval Estimate, and Confidence Interval403
  • Maximum Likelihood Estimation405
  • Minimum Mean Squared Error Estimation408
  • Hypothesis Testing411
  • Hypothesis Test Procedure412
  • Type I and Type II Errors413
  • One-Tailed and Two-Tailed Tests413
  • Curve Fitting and Linear Regression418
  • Chapter Summary422
  • Problems422
  • Appendix 1: Table for the CDF of the Standard Normal Random Variable427
  • Bibliography429
  • Index433
Book details
  • Vendor Elsevier S & T
  • SKU 9780120885084
  • ISBN-13 9780080492704

Do you have questions about this book?

Ask an expert!

Description eBook delivery & access Reviews
This book is based on the premise that engineers use probability as a modeling tool, and that probability can be applied to the solution of engineering problems. Engineers and students studying probability and random processes also need to analyze data, and thus need some knowledge of statistics. This book is designed to provide students with a thorough grounding in probability and stochastic processes, demonstrate their applicability to real-world problems, and introduce the basics of statistics. The book's clear writing style and homework problems make it ideal for the classroom or for self-study.

* Good and solid introduction to probability theory and stochastic processes
* Logically organized; writing is presented in a clear manner
* Choice of topics is comprehensive within the area of probability
* Ample homework problems are organized into chapter sections