Introduction to Probability

INTRODUCTION 1 POSSIBILITIES Introduction Tree Diagrams Multiplication Rules Permutations Factorials Indistinguishable Objects Combinations Binomial Coefficients 2 PROBABILITIES Introduction The Classical Concept Probabilities and Odds The Frequency Interpretation Subjective Probabilities Summary 3 EXPECTATIONS Introduction Mathematical Expectation Expectations and Subjective Probabilities Utility Decision Making 4 EVENTS Introduction The Sample Space Events Compound Events The Number of Elements in a Set 5 RULES OF PROBABILITY Introduction The Postulates of Probability Probability Measures Some Further Rules General Addition Rules 6 CONDITIONAL PROBABILITIES Introduction Conditional Probability Multiplication Rules Rule of Elimination Bayes' Rule 7 PROBABILITY DISTRIBUTIONS Introduction Probability Functions The Mean The Binomial Distribution Binomial Tables A Bayesian Application The Hypergeometric Distribution The Geometric Distribution The Multinomial Distribution 8 THE LAW OF LARGE NUMBERS Introduction The Standard Deviation Chebyshev's Theorem The Law of Large Numbers Technical Note SUMMARY BIBLIOGRAPHY TABLES ANSWERS TO ODD-NUMBERED EXERCISES INDEX