UID:
almafu_9958068915202883
Format:
1 online resource (457 p.)
Edition:
Second edition.
ISBN:
9780128010358
,
0128010355
Content:
e it ideal for the classroom or for self-study. The book: demonstrates concepts with more than 100 illustrations, including 2 dozen new drawings; expands readers' understanding of disruptive statistics in a new chapter (chapter 8); provides a new chapter on Introduction to Random Processes with 14 new illustrations and tables explaining key concepts; includes two chapters devoted to the two branches of statistics, namely descriptive statistics (chapter 8) and inferential (or inductive) statistics (chapter 9). --
Note:
Bibliographic Level Mode of Issuance: Monograph
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Front Cover -- Fundamentals of Applied Probability and Random Processes -- Copyright -- Contents -- Acknowledgment -- Preface to the Second Edition -- Preface to First Edition -- Chapter 1: Basic Probability Concepts -- 1.1. Introduction -- 1.2. Sample Space and Events -- 1.3. Definitions of Probability -- 1.3.1. Axiomatic Definition -- 1.3.2. Relative-Frequency Definition -- 1.3.3. Classical Definition -- 1.4. Applications of Probability -- 1.4.1. Information Theory -- 1.4.2. Reliability Engineering -- 1.4.3. Quality Control -- 1.4.4. Channel Noise -- 1.4.5. System Simulation -- 1.5. Elementary Set Theory -- 1.5.1. Set Operations -- 1.5.2. Number of Subsets of a Set -- 1.5.3. Venn Diagram -- 1.5.4. Set Identities -- 1.5.5. Duality Principle -- 1.6. Properties of Probability -- 1.7. Conditional Probability -- 1.7.1. Total Probability and the Bayes Theorem -- 1.7.2. Tree Diagram -- 1.8. Independent Events -- 1.9. Combined Experiments -- 1.10. Basic Combinatorial Analysis -- 1.10.1. Permutations -- 1.10.2. Circular Arrangement -- 1.10.3. Applications of Permutations in Probability -- 1.10.4. Combinations -- 1.10.5. The Binomial Theorem -- 1.10.6. Stirling's Formula -- 1.10.7. The Fundamental Counting Rule -- 1.10.8. Applications of Combinations in Probability -- 1.11. Reliability Applications -- 1.12. Chapter Summary -- 1.13. Problems -- Section 1.2. Sample Space and Events -- Section 1.3. Definitions of Probability -- Section 1.5. Elementary Set Theory -- Section 1.6. Properties of Probability -- Section 1.7. Conditional Probability -- Section 1.8. Independent Events -- Section 1.10. Combinatorial Analysis -- Section 1.11. Reliability Applications -- Chapter 2: Random Variables -- 2.1. Introduction -- 2.2. Definition of a Random Variable -- 2.3. Events Defined by Random Variables -- 2.4. Distribution Functions -- 2.5. Discrete Random Variables.
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2.5.1. Obtaining the PMF from the CDF -- 2.6. Continuous Random Variables -- 2.7. Chapter Summary -- 2.8. Problems -- Section 2.4. Distribution Functions -- Section 2.5. Discrete Random Variables -- Section 2.6. Continuous Random Variables -- Chapter 3: Moments of Random Variables -- 3.1. Introduction -- 3.2. Expectation -- 3.3. Expectation of Nonnegative Random Variables -- 3.4. Moments of Random Variables and the Variance -- 3.5. Conditional Expectations -- 3.6. The Markov Inequality -- 3.7. The Chebyshev Inequality -- 3.8. Chapter Summary -- 3.9. Problems -- Section 3.2. Expected Values -- Section 3.4. Moments of Random Variables and the Variance -- Section 3.5. Conditional Expectations -- Sections 3.6 and 3.7. Markov and Chebyshev Inequalities -- Chapter 4: Special Probability Distributions -- 4.1. Introduction -- 4.2. The Bernoulli Trial and Bernoulli Distribution -- 4.3. Binomial Distribution -- 4.4. Geometric Distribution -- 4.4.1. CDF of the Geometric Distribution -- 4.4.2. Modified Geometric Distribution -- 4.4.3. ``Forgetfulness´´ Property of the Geometric Distribution -- 4.5. Pascal Distribution -- 4.5.1. Distinction Between Binomial and Pascal Distributions -- 4.6. Hypergeometric Distribution -- 4.7. Poisson Distribution -- 4.7.1. Poisson Approximation of the Binomial Distribution -- 4.8. Exponential Distribution -- 4.8.1. ``Forgetfulness´´ Property of the Exponential Distribution -- 4.8.2. Relationship between the Exponential and Poisson Distributions -- 4.9. Erlang Distribution -- 4.10. Uniform Distribution -- 4.10.1. The Discrete Uniform Distribution -- 4.11. Normal Distribution -- 4.11.1. Normal Approximation of the Binomial Distribution -- 4.11.2. The Error Function -- 4.11.3. The Q-Function -- 4.12. The Hazard Function -- 4.13. Truncated Probability Distributions -- 4.13.1. Truncated Binomial Distribution.
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4.13.2. Truncated Geometric Distribution -- 4.13.3. Truncated Poisson Distribution -- 4.13.4. Truncated Normal Distribution -- 4.14. Chapter Summary -- 4.15. Problems -- Section 4.3. Binomial Distribution -- Section 4.4. Geometric Distribution -- Section 4.5. Pascal Distribution -- Section 4.6. Hypergeometric Distribution -- Section 4.7. Poisson Distribution -- Section 4.8. Exponential Distribution -- Section 4.9. Erlang Distribution -- Section 4.10. Uniform Distribution -- Section 4.11. Normal Distribution -- Chapter 5: Multiple Random Variables -- 5.1. Introduction -- 5.2. Joint CDFs of Bivariate Random Variables -- 5.2.1. Properties of the Joint CDF -- 5.3. Discrete Bivariate Random Variables -- 5.4. Continuous Bivariate Random Variables -- 5.5. Determining Probabilities from a Joint CDF -- 5.6. Conditional Distributions -- 5.6.1. Conditional PMF for Discrete Bivariate Random Variables -- 5.6.2. Conditional PDF for Continuous Bivariate Random Variables -- 5.6.3. Conditional Means and Variances -- 5.6.4. Simple Rule for Independence -- 5.7. Covariance and Correlation Coefficient -- 5.8. Multivariate Random Variables -- 5.9. Multinomial Distributions -- 5.10. Chapter Summary -- 5.11. Problems -- Section 5.3. Discrete Bivariate Random Variables -- Section 5.4. Continuous Bivariate Random Variables -- Section 5.6. Conditional Distributions -- Section 5.7. Covariance and Correlation Coefficient -- Section 5.9. Multinomial Distributions -- Chapter 6: Functions of Random Variables -- 6.1. Introduction -- 6.2. Functions of One Random Variable -- 6.2.1. Linear Functions -- 6.2.2. Power Functions -- 6.3. Expectation of a Function of One Random Variable -- 6.3.1. Moments of a Linear Function -- 6.3.2. Expected Value of a Conditional Expectation -- 6.4. Sums of Independent Random Variables -- 6.4.1. Moments of the Sum of Random Variables.
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6.4.2. Sum of Discrete Random Variables -- 6.4.3. Sum of Independent Binomial Random Variables -- 6.4.4. Sum of Independent Poisson Random Variables -- 6.4.5. The Spare Parts Problem -- 6.5. Minimum of Two Independent Random Variables -- 6.6. Maximum of Two Independent Random Variables -- 6.7. Comparison of the Interconnection Models -- 6.8. Two Functions of Two Random Variables -- 6.8.1. Application of the Transformation Method -- 6.9. Laws of Large Numbers -- 6.10. The Central Limit Theorem -- 6.11. Order Statistics -- 6.12. Chapter Summary -- 6.13. Problems -- Section 6.2. Functions of One Random Variable -- Section 6.4. Sums of Random Variables -- Sections 6.4 and 6.5. Maximum and Minimum of Independent Random Variables -- Section 6.8. Two Functions of Two Random Variables -- Section 6.10. The Central Limit Theorem -- Section 6.11. Order Statistics -- Chapter 7: Transform Methods -- 7.1. Introduction -- 7.2. The Characteristic Function -- 7.2.1. Moment-Generating Property of the Characteristic Function -- 7.2.2. Sums of Independent Random Variables -- 7.2.3. The Characteristic Functions of Some Well-Known Distributions -- 7.3. The s-Transform -- 7.3.1. Moment-Generating Property of the s-Transform -- 7.3.2. The s-Transform of the PDF of the Sum of Independent Random Variables -- 7.3.3. The s-Transforms of Some Well-Known PDFs -- 7.4. The z-Transform -- 7.4.1. Moment-Generating Property of the z-Transform -- 7.4.2. The z-Transform of the PMF of the Sum of Independent Random Variables -- 7.4.3. The z-Transform of Some Well-Known PMFs -- 7.5. Random Sum of Random Variables -- 7.6. Chapter Summary -- 7.7. Problems -- Section 7.2. Characteristic Functions -- Section 7.3. s-Transforms -- Section 7.4. z-Transforms -- Section 7.5. Random Sum of Random Variables -- Chapter 8: Introduction to Descriptive Statistics -- 8.1. Introduction.
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8.2. Descriptive Statistics -- 8.3. Measures of Central Tendency -- 8.3.1. Mean -- 8.3.2. Median -- 8.3.3. Mode -- 8.4. Measures of Dispersion -- 8.4.1. Range -- 8.4.2. Quartiles and Percentiles -- 8.4.3. Variance -- 8.4.4. Standard Deviation -- 8.5. Graphical and Tabular Displays -- 8.5.1. Dot Plots -- 8.5.2. Frequency Distribution -- 8.5.3. Histograms -- 8.5.4. Frequency Polygons -- 8.5.5. Bar Graphs -- 8.5.6. Pie Chart -- 8.5.7. Box and Whiskers Plot -- 8.6. Shape of Frequency Distributions: Skewness -- 8.7. Shape of Frequency Distributions: Peakedness -- 8.8. Chapter Summary -- 8.9. Problems -- Section 8.3. Measures of Central Tendency -- Section 8.4. Measures of Dispersion -- Section 8.6. Graphical Displays -- Section 8.7. Shape of Frequency Distribution -- Chapter 9: Introduction to Inferential Statistics -- 9.1. Introduction -- 9.2. Sampling Theory -- 9.2.1. The Sample Mean -- 9.2.2. The Sample Variance -- 9.2.3. Sampling Distributions -- 9.3. Estimation Theory -- 9.3.1. Point Estimate, Interval Estimate, and Confidence Interval -- 9.3.2. Maximum Likelihood Estimation -- 9.3.3. Minimum Mean Squared Error Estimation -- 9.4. Hypothesis Testing -- 9.4.1. Hypothesis Test Procedure -- 9.4.2. Type I and Type II Errors -- 9.4.3. One-Tailed and Two-Tailed Tests -- 9.5. Regression Analysis -- 9.6. Chapter Summary -- 9.7. Problems -- Section 9.2. Sampling Theory -- Section 9.3. Estimation Theory -- Section 9.4. Hypothesis Testing -- Section 9.5. Regression Analysis -- Chapter 10: Introduction to Random Processes -- 10.1. Introduction -- 10.2. Classification of Random Processes -- 10.3. Characterizing a Random Process -- 10.3.1. Mean and Autocorrelation Function -- 10.3.2. The Autocovariance Function -- 10.4. Crosscorrelation and Crosscovariance Functions -- 10.4.1. Review of Some Trigonometric Identities -- 10.5. Stationary Random Processes.
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10.5.1. Strict-Sense Stationary Processes.
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English
Additional Edition:
ISBN 9780128008522
Additional Edition:
ISBN 0128008520
Language:
English
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