Introduction to Probability and Its Applications

Richard L. Scheaffer, Professor Emeritus of Statistics, University of Florida, received his Ph.D. in statistics from Florida State University. Accompanying a career of teaching, research and administration, Dr. Scheaffer has led efforts on the improvement of statistics education throughout the school and college curriculum. Co-author of five textbooks, he was one of the developers of the Quantitative Literacy Project that formed the basis of the data analysis strand in the curriculum standards of the National Council of Teachers of Mathematics. He also led the task force that developed the AP Statistics Program, for which he served as Chief Faculty Consultant. Dr. Scheaffer is a Fellow and past president of the American Statistical Association, a past chair of the Conference Board of the Mathematical Sciences, and an advisor on numerous statistics education projects.

• 1. PROBABILITY AND THE WORLD AROUND USWhy Study Probability / Deterministic and Probabilistic Models / Applications of Probability / A Brief Historical Note / A Look Ahead2. PROBABILITYUnderstanding Randomness: An Intuitive Notion of Probability / A Brief Review of Set Notation / Definition of Probability / Counting Rules Useful in Probability / Conditional Probability and Independence / Rules of Probability / Odds, Odds Ratios, and Relative Risk / Activities for Students: Simulation / Summary / Supplementary Exercises3. DISCRETE PROBABILITY DISTRIBUTIONSRandom Variables and Their Probability Distributions / Expected Values of Random Variables / The Bernoulli Distributions / The Binomial Distribution / The Geometric Distribution / The Negative Binomial Distribution / The Poisson Distribution / The Hypergeometric Distribution / The Moment-generating Functions / The Probability-generating Function / Markov Chains / Activities for Students: Simulation / Summary / Supplementary Exercises4. CONTINUOUS PROBABILITY DISTRIBUTIONSContinuous Random Variables and Their Probability Distributions / Expected Values of Continuous Random Variables / The Uniform Distribution / The Exponential Distribution / The Gamma Distribution / The Normal Distribution / The Beta Distribution / The Weibull Distribution / Reliability / Moment-generating Functions for Continuous Random Variables / Expectations of Discontinuous Functions and Mixed Probability Distributions / Activities for Students: Simulation / Summary / Supplementary Exercises5. MULTIVARIATE PROBABILITY DISTRIBUTIONSBivariate and Marginal Probability Distributions / Conditional Probability Distributions / Independent Random Variables / Expected Values of Functions of Random Variables / The Multinomial Distribution / More on the Moment-generating Function / Conditional Expectations / Compounding and its Applications / Summary / Supplementary Exercises6. FUNCTIONS OF RANDOM VARIABLESIntroduction / Method of Distribution Functions / Method of Transformations / Method of Conditioning / Method of Moment-generating Functions / Order Statistics / Probability-generating Functions: Applications to Random Sums of Random Variables / Summary / Supplementary Exercises7. SOME APPROXIMATIONS TO PROBABILITY DISTRIBUTIONS: LIMIT THEOREMSIntroduction / Convergence in Probability / Convergence in Distribution / The Central Limit Theorem / Combination of Convergence in Probability and Convergence in Distribution / Summary / Supplementary Exercises8. EXTENDED APPLICATIONS OF PROBABILITYThe Poisson Process / Birth and Death Processes: Biological Applications / Queues: Engineering Applications / Arrival Times for the Poisson Process / Infinite Server Queue / Renewal Theory: Reliability Applications / Summary / Exercises / APPENDIX TABLES / NOTES ON COMPUTER SIMULATIONS / REFERENCES / ANSWERS TO SELECTED EXERCISES / INDEX