## Table of contents for Introduction to probability with R / Kenneth Baclawski.

Bibliographic record and links to related information available from the Library of Congress catalog.

Note: Contents data are machine generated based on pre-publication provided by the publisher. Contents may have variations from the printed book or be incomplete or contain other coding. ```
Preface 1
1 Sets, Events and Probability 5
1.1 The Algebra of Sets 6
1.2 The Bernoulli Sample Space 9
1.3 The Algebra of Multisets 11
1.4 The Concept of Probability 12
1.5 Properties of Probability Measures 13
1.6 Independent Events 15
1.7 The Bernoulli Process 16
1.8 The R Language 17
1.9 Exercises 23
1.10 Answers to Selected Exercises 26
2 Finite Processes 33
2.1 The Basic Models 34
2.2 Counting Rules 35
2.3 Computing Factorials 36
2.4 The Second Rule of Counting 37
2.5 Computing Probabilities. 39
2.6 Answers to Selected Exercises 46
3 Discrete Random Variables 51
3.1 The Bernoulli Process: Tossing a coin 53
3.2 The Bernoulli Process: Random Walk 64
3.3 Independence and Joint Distributions 65
3.4 Expectations 68
3.5 The Inclusion-Exclusion Principle 70
3.6 Exercises 75
3.7 Answers to Selected Exercises 79
4 General Random Variables 91
4.1 Order Statistics 95
4.2 The Concept of a General Random Variable 97
4.3 Joint Distribution and Joint Density 100
4.4 Mean, Median and Mode 100
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ii CONTENTS
4.5 The Uniform Process 102
4.6 Table of Probability Distributions 106
4.7 Scale Invariance 108
4.8 Exercises 110
4.9 Answers to Selected Exercises 115
5 Statistics and the Normal Distribution 123
5.1 Variance 124
5.2 Bell-Shaped Curve 130
5.3 The Central Limit Theorem 132
5.4 Significance Levels 137
5.5 Confidence Intervals 139
5.6 The Law of Large Numbers 141
5.7 The Cauchy Distribution 144
5.8 Exercises 148
5.9 Answers to Selected Exercises 158
6 Conditional Probability 169
6.1 Discrete Conditional Probability 170
6.2 Gaps and Runs in the Bernoulli Process 174
6.3 Sequential Sampling 177
6.4 Continuous Conditional Probability 181
6.5 Conditional Densities 184
6.6 Gaps in the Uniform Process 186
6.7 The Algebra of Probability Distributions 190
6.8 Exercises 195
6.9 Answers to Selected Exercises 203
7 The Poisson Process 213
7.1 Continuous Waiting Times 213
7.2 Comparing Bernoulli with Uniform 219
7.3 The Poisson Sample Space 224
7.4 Consistency of the Poisson Process 231
7.5 Exercises 233
7.6 Answers to Selected Exercises 239
8 Randomization and Compound Processes 245
8.1 Randomized Bernoulli Process 246
8.2 Randomized Uniform Process 247
8.3 Randomized Poisson Process 249
8.4 Proof of the Central Limit Theorem 251
8.5 Laplace Transforms and Renewal Processes 252
8.6 Randomized Sampling Processes 256
8.7 Prior and Posterior Distributions 257
8.8 Reliability Theory 260
CONTENTS iii
8.9 Bayesian Networks 263
8.10 Exercises 268
8.11 Answers to Selected Exercises 270
9 Entropy and Information 279
9.1 Discrete Entropy 279
9.2 The Shannon Coding Theorem 287
9.3 Continuous Entropy 289
9.4 Proofs of Shannon¿s Theorems 297
9.5 Exercises 301
9.6 Answers to Selected Exercises 303
10 Markov Chains 307
10.1 The Markov Property 307
10.2 The Ruin Problem 311
10.3 The Network of a Markov Chain 316
10.4 The Evolution of a Markov Chain 317
10.5 The Markov Sample Space 322
10.6 Invariant Distributions 325
10.7 Monte Carlo Markov Chains 331
10.8 Exercises 334
10.9 Answers to Selected Exercises 336
A Random Walks 347
A.1 Fluctuations of Random Walks 347
A.2 The Arcsine Law of Random Walks 351
B Memorylessness and Scale-Invariance 355
B.1 Memorylessness 355
B.2 Self-Similarity 356
References 359
Index 360
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Library of Congress Subject Headings for this publication:

Probabilities.
R (Computer program language) -- Mathematical models.