The Probability Tutoring Book: An Intuitive Course for Engineers and Scientists

Preface Vll
Introduction IX

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1 Basic Probability 1
...1-1 Probability Spaces 1
...1-2 Counting Techniques 6
...1-3 Counting Techniques Continued 14
...1-4 ORs and AT LEASTs 20
...1-5 Continuous Uniform Distributions 30
...Review for the Next Chapter 36

2 Independent Trials and 2-Stage Experiments 37
...2-1 Conditional Probability and Independent Events 37
...2-2 The Binomial and Multinomial Distributions 46
...2-3 Simulating an Experiment 53
...2-4 The Theorem of Total Probability and Bayes\' Theorem 56
...2-5 The Poisson Distribution 63
...Review Problems for Chapters 1 and 2 68

3 Expectation 74
...3-1 Expected Value of a Random Variable 74
...3-2 The Method of Indicators 77
...3-3 Conditional Expectation and the Theorem of Total Expectation 85
...3-4 Variance 91
...Review Problems for Chapter 3 92
...Review for the Next Chapter 95


4 Continuous Random Variables 97
...4-1 Density Functions 97
...4-2 Distribution Functions 104
...4-3 The Exponential Distribution 120
...4-4 The Normal (Gaussian) Distribution 127
...4-5 The Election Problem 138
...4-6 Functions of a Random Variable 141
...4-7 Simulating a Random Variable 158
...Review for the Next Chapter 164

5 Jointly Distributed Random Variables 171
...5-1 Joint Densities 171
...5-2 Marginal Densities 182
...5-3 Functions of Several Random Variables 192
...Review Problems for Chapters 4 and 5 197

6 Jointly Distributed Random Variables Continued 201
...6-1 Sums of Independent Random Variables 201
...6-2 Order Statistics 207

7 Expectation Again 213
...7-1 Expectation of a Random Variable 213
...7-2 Variance 223
...7-3 Correlation 235

8 Conditional Probability 242
...8-1 Conditional Densities 242
...8-2 2-Stage Experiments 250
...8-3 Mixed 2-Stage Experiments 257
...Review Problems for Chapters 6, 7, and 8 263

9 Limit Theorems 266
...9-1 The Central Limit Theorem 266
...9-2 The Weak Law of Large Numbers 269
...Review Problems for Chapters 4-9 274

Solutions 275
Index 466