Probably Not

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 About The Companion Site Introduction 1 An Introduction to Probability Predicting The Future Rule Making Random Events and Probability The Lottery Coin Flipping The Coin Flip Strategy That Can't Lose The Prize Behind The Door The Checker Board Comments Problems 2 Probability Distribution Functions and Some Math Basics The Probability Distribution Function Averages and Weighted Averages Expected Values The Basic Coin Flip Game PDF Symmetry Standard Deviation Cumulative Distribution Function The Confidence Interval Final Points Rehash and Histograms Problems 3 Building A Bell Problems 4 Random Walks The One-Dimensional Random Walk Some Subsequent Calculations Diffusion Problems 5 Life Insurance Introduction Life Insurance Insurance As Gambling Life Tables Birth Rates and Population Stability Life Tables, Again Premiums Social Security - Sooner Or Later? Problems 6 The Binomial Theorem Introduction The Binomial Probability Formula Permutations and Combinations Large Number Approximations The Poisson Distribution Disease Clusters Clusters Problems 7 Pseudorandom Numbers and Monte -Carlo Simulations Random Numbers and Simulations Pseudo-Random Numbers The Middle Square PRNG The Linear Congruential PRNG A Normal Distribution Generator An Arbitrary Distribution Generator Monte Carlo Simulations A League of Our Own Discussion Notes 8 Some Gambling Games In Detail The Basic Coin Flip Game The "Ultimate Winning Strategy" Parimutuel Betting The Gantt Chart and A Hint of Another Approach Problems 9 Scheduling and Waiting Introduction Scheduling Appointments In The Doctor's Office Lunch with A Friend Waiting for A Bus Problems 10 Combined and Conditional Probabilities Introduction Functional Notation (Again) Conditional Probability Medical Test Results The Shared Birthday Problem Problems 11 Bayesian Statistics Bayes Theorem Multiple Possibilities Will Monty Hall Ever Go Away? Philosophy The Prosecutor's Fallacy Continuous Functions Credible Intervals Gantt Charts (Again) Problems 12 Estimation Problems The Number of Locomotives Problem Number of Locomotives, Improved Estimate Decision Making The Light House Problem The Likelihood Function The Light House Problem II 13 Two Paradoxes Introduction Parrondo's Paradox Another Parrondo Game The Parrondo Ratchet Simpson's Paradox Problems 14 Benford's Law Introduction History The 1/x Distribution Goodness of Fit Measure Smith's Analysis Problems 15 Networks, Infectious Diseases and Chain Letters Introduction Degrees of Separation Propagation Along The Networks Some Other Networks Neighborhood Chains Chain Letters Comments 16 Introduction To Frequentist Statistical Inference Introduction Sampling Sample Distributions and Standard Deviations Estimating Population Average From A Sample The Student-T Distribution Polling Statistics Did A Sample Come From A Given Distribution? A Little Reconciliation Correlation and Causality Correlation Coefficient Regression Lines Regression To The Mean Problems 17 Statistical Mechanics and Thermodynamics Introduction Statistical Mechanics (Concepts of) Thermodynamics 18 Chaos and Quanta Introduction Chaos Probability In Quantum Mechanic Appendix Introduction Continuous Distributions and Integrals Exponential Functions Index