Chapter1 Probability 1
1.3.3 Generating Values from an Arbitrary Distribution 17
1.7.3 Chernoff Bound 37
1.9 Further Reading 47
1.10 Exercises 47
Chapter2 Statistics 53
2.4 Testing Hypotheses about Outcomes of Experiments 70
2.4.1 Hypothesis Testing 71
2.4.2 Errors in Hypothesis Testing 72
2.4.3 Formulating a Hypothesis 73
2.4.4 Comparing an Outcome with a Fixed Quantity 74
2.4.5 Comparing Outcomes from Two Experiments 76
2.4.6 Testing Hypotheses about Quantities Measured on Ordinal Scales 79
2.4.7 Fitting a Distribution 82
2.4.8 Power 85
2.5 Independence and Dependence: Regression and Correlation 86
2.5.1 Independence 86
2.5.2 Regression 88
2.5.3 Correlation 90
2.6 Comparing Multiple Outcomes Simultaneously: Analysis of Variance 95
2.6.1 One-Way Layout 95
2.6.2 Multiway Layouts 98
2.7 Design of Experiments 99
2.8 Dealing with Large Data Sets 100
2.9 Common Mistakes in Statistical Analysis 103
2.9.1 Defining Population 103
2.9.2 Lack of Confidence Intervals in Comparing Results 103
2.9.3 Not Stating the Null Hypothesis 103
2.9.4 Too Small a Sample 104
2.9.5 Too Large a Sample 104
2.9.6 Not Controlling All Variables When Collecting Observations 104
2.9.7 Converting Ordinal to Interval Scales 104
2.9.8 Ignoring Outliers 105
2.10 Further Reading 105
2.11 Exercises
Chapter3 Linear Algebra 109
3.7 Exercises 143
Chapter4 Optimization 147
4.8 Exercises 170
Chapter5 Signals, Systems, and Transforms 173
5.11 Further Reading 233
5.12 Exercises 234
Chapter6 Stochastic Processes and Queueing Theory 237
6.8 Further Reading 272
6.9 Exercises 272
Chapter7 Game Theory 277
7.5 Further Reading 315
7.6 Exercises 316
Chapter8 Elements of Control Theory 319
8.8.3 Placing System Roots 357
8.11 Partial Fraction Expansion 367
8.11.1 Distinct Roots 367
8.11.2 Complex Conjugate Roots 368
8.11.3 Repeated Roots 369
8.12 Further Reading 370
8.13 Exercises 370
Chapter9 Information Theory 373
9.7 Further Reading 407
9.8 Exercises 407