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E-raamat: Probably Not: Future Prediction Using Probability and Statistical Inference

(Motorola, Inc.)
  • Formaat: PDF+DRM
  • Ilmumisaeg: 26-Jul-2019
  • Kirjastus: John Wiley & Sons Inc
  • Keel: eng
  • ISBN-13: 9781119518136
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  • Formaat: PDF+DRM
  • Ilmumisaeg: 26-Jul-2019
  • Kirjastus: John Wiley & Sons Inc
  • Keel: eng
  • ISBN-13: 9781119518136
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A revised edition that explores random numbers, probability, and statistical inference at an introductory mathematical level

Written in an engaging and entertaining manner, the revised and updated second edition of Probably Not continues to offer an informative guide to probability and prediction. The expanded second edition contains problem and solution sets. In addition, the book’s illustrative examples reveal how we are living in a statistical world, what we can expect, what we really know based upon the information at hand and explains when we only think we know something.

The author introduces the principles of probability and explains probability distribution functions. The book covers combined and conditional probabilities and contains a new section on Bayes Theorem and Bayesian Statistics, which features some simple examples including the Presecutor’s Paradox, and Bayesian vs. Frequentist thinking about statistics. New to this edition is a chapter on Benford’s Law that explores measuring the compliance and financial fraud detection using Benford’s Law. This book:

  • Contains relevant mathematics and examples that demonstrate how to use the concepts presented
  • Features a new chapter on Benford’s Law that explains why we find Benford’s law upheld in so many, but not all, natural situations
  • Presents updated Life insurance tables
  • Contains updates on the Gantt Chart example that further develops the discussion of random events
  • Offers a companion site featuring solutions to the problem sets within the book

Written for mathematics and statistics students and professionals, the updated edition of Probably Not: Future Prediction Using Probability and Statistical Inference, Second Edition combines the mathematics of probability with real-world examples.

LAWRENCE N. DWORSKY, PhD, is a retired Vice President of the Technical Staff and Director of Motorola’s Components Research Laboratory in Schaumburg, Illinois, USA. He is the author of Introduction to Numerical Electrostatics Using MATLAB from Wiley.

Acknowledgments xi
About the Companion Website xiii
Introduction 1(4)
1 An Introduction to Probability 5(30)
Predicting the Future
5(2)
Rule Making
7(2)
Random Events and Probability
9(6)
The Lottery (Very Improbable Events and Very Large Data Sets)
15(2)
Coin Flipping (Fair Games, Looking Backward for Insight)
17(7)
The Coin Flip Strategy That Can't Lose
24(1)
The Prize Behind the Door (Looking Backward for Insight, Again)
25(2)
The Checker Board (Dealing With Only Part of the Data Set(
27(4)
Comments
31(1)
Problems
32(3)
2 Probability Distribution Functions and Some Math Basics 35(36)
The Probability Distribution Function
35(3)
Averages and Weighted Averages
38(3)
Expected Values (Again)
41(2)
The Basic Coin Flip Game
43(1)
PDF Symmetry
43(3)
Standard Deviation
46(9)
Cumulative Distribution Function
55(2)
The Confidence Interval
57(1)
Final Points
58(1)
Rehash and Histograms
59(7)
Problems
66(5)
3 Building a Bell 71(18)
Problems
87(2)
4 Random Walks 89(14)
The One-Dimensional Random Walk
89(4)
Some Subsequent Calculations
93(2)
Diffusion
95(4)
Problems
99(4)
5 Life Insurance 103(26)
Introduction
103(1)
Life Insurance
103(1)
Insurance as Gambling
104(3)
Life Tables
107(5)
Birth Rates and Population Stability
112(1)
Life Tables, Again
113(2)
Premiums
115(5)
Social Security - Sooner or Later?
120(5)
Problems
125(4)
6 The Binomial Theorem 129(16)
Introduction
129(1)
The Binomial Probability Formula
130(2)
Permutations and Combinations
132(2)
Large Number Approximations
134(2)
The Poisson Distribution
136(4)
Disease Clusters
140(1)
Clusters
140(2)
Problems
142(3)
7 Pseudorandom Numbers and Monte Carlo Simulations 145(16)
Random Numbers and Simulations
145(1)
Pseudorandom Numbers
145(1)
The Middle Square PRNG
146(2)
The Linear Congruential PRNG
148(2)
A Normal Distribution Generator
150(1)
An Arbitrary Distribution Generator
151(2)
Monte Carlo Simulations
153(3)
A League of Our Own
156(3)
Discussion
159(1)
Notes
160(1)
8 Some Gambling Games in Detail 161(16)
The Basic Coin Flip Game
161(5)
The "Ultimate Winning Strategy"
166(3)
Parimutuel Betting
169(3)
The Gantt Chart and a Hint of Another Approach
172(2)
Problems
174(3)
9 Scheduling and Waiting 177(10)
Introduction
177(1)
Scheduling Appointments in the Doctor's Office
177(3)
Lunch with a Friend
180(2)
Waiting for a Bus
182(3)
Problems
185(2)
10 Combined and Conditional Probabilities 187(12)
Introduction
187(1)
Functional Notation (Again)
187(2)
Conditional Probability
189(3)
Medical Test Results
192(3)
The Shared Birthday Problem
195(2)
Problems
197(2)
11 Bayesian Statistics 199(22)
Bayes Theorem
199(3)
Multiple Possibilities
202(5)
Will Monty Hall Ever Go Away?
207(2)
Philosophy
209(1)
The Prosecutor's Fallacy
210(1)
Continuous Functions
211(3)
Credible Intervals
214(1)
Gantt Charts (Again)
215(2)
Problems
217(4)
12 Estimation Problems 221(12)
The Number of Locomotives Problem
221(1)
Number of Locomotives, Improved Estimate
222(2)
Decision Making
224(3)
The Lighthouse Problem
227(2)
The Likelihood Function
229(3)
The Lighthouse Problem II
232(1)
13 Two Paradoxes 233(14)
Introduction
233(1)
Parrondo's Paradox
233(3)
Another Parrondo Game
236(3)
The Parrondo Ratchet
239(1)
Simpson's Paradox
240(4)
Problems
244(3)
14 Benford's Law 247(14)
Introduction
247(1)
History
247(2)
The 1/x Distribution
249(3)
Surface Area of Countries of the World
252(1)
Goodness of Fit Measure
253(2)
Smith's Analysis
255(4)
Problems
259(2)
15 Networks, Infectious Diseases, and Chain Letters 261(16)
Introduction
261(1)
Degrees of Separation
261(4)
Propagation Along the Networks
265(5)
Some Other Networks
270(1)
Neighborhood Chains
271(2)
Chain Letters
273(3)
Comments
276(1)
16 Introduction to Frequentist Statistical Inference 277(26)
Introduction
277(1)
Sampling
277(3)
Sample Distributions and Standard Deviations
280(2)
Estimating Population Average from a Sample
282(3)
The Student-T Distribution
285(4)
Did a Sample Come from a Given Population?
289(1)
A Little Reconciliation
289(2)
Correlation and Causality
291(2)
Correlation Coefficient
293(1)
Regression Lines
294(1)
Regression to the Mean
295(3)
Problems
298(5)
17 Statistical Mechanics and Thermodynamics 303(8)
Introduction
303(1)
Statistical Mechanics
304(2)
(Concepts of) Thermodynamics
306(5)
18 Chaos and Quanta 311(12)
Introduction
311(1)
Chaos
311(8)
Probability in Quantum Mechanics
319(4)
Appendix 323(6)
Index 329
LAWRENCE N. DWORSKY, PHD, is a retired Vice President of the Technical Staff and Director of Motorola's Components Research Laboratory in Schaumburg, Illinois, USA. He is the author of Introduction to Numerical Electrostatics Using MATLAB® from Wiley.