Introduction to Probability and Its Applications

PROBABILITY AND THE WORLD AROUND US Why Study Probability / Deterministic and Probabilistic Models / Applications of Probability / A Brief Historical Note / A Look Ahead 2. PROBABILITY Understanding 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 Exercises 3. DISCRETE PROBABILITY DISTRIBUTIONS Random 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 Exercises 4. CONTINUOUS PROBABILITY DISTRIBUTIONS Continuous 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 Exercises 5. MULTIVARIATE PROBABILITY DISTRIBUTIONS Bivariate 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 Exercises 6. FUNCTIONS OF RANDOM VARIABLES Introduction / 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 Exercises 7. SOME APPROXIMATIONS TO PROBABILITY DISTRIBUTIONS: LIMIT THEOREMS Introduction / Convergence in Probability / Convergence in Distribution / The Central Limit Theorem / Combination of Convergence in Probability and Convergence in Distribution / Summary / Supplementary Exercises 8. EXTENDED APPLICATIONS OF PROBABILITY The 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