
Probability in the World Around Us 


1  (5) 


1  (1) 

Deterministic and Probabilistic Models 


2  (1) 

Applications of Probability 


3  (2) 


5  (1) 


5  (1) 


6  (61) 

Understanding Randomness: An Intuitive Notion of Probability 


6  (3) 

A Brief Review of Set Notation 


9  (4) 

Definition of Probability 


13  (8) 

Counting Rules Useful in Probability 


21  (11) 

Conditional Probability and Independence 


32  (8) 


40  (17) 

Odds, Odds Ratios, and Relative Risk 


57  (3) 

Activities for Students: Simulation 


60  (2) 


62  (5) 


62  (5) 

Discrete ProbabilityDistributions 


67  (71) 

Random Variables and Their Probability Distributions 


67  (6) 

Expected Values of Random Variables 


73  (13) 

The Bernoulli Distribution 


86  (1) 

The Binomial Distribution 


87  (10) 

The Geometric Distribution 


97  (3) 

The Negative Binomial Distribution 


100  (4) 


104  (5) 

The Hypergeometric Distribution 


109  (6) 

The MomentGenerating Function 


115  (2) 

The Probabilitygenerating Function 


117  (3) 


120  (8) 

Activities for Students: Simulation 


128  (5) 


133  (5) 


134  (4) 

Continuous Probability Distributions 


138  (85) 

Continuous Random Variables and Their Probability Distributions 


138  (8) 

Expected Values of Continuous Random Variables 


146  (5) 


151  (5) 

The Exponential Distribution 


156  (6) 


162  (5) 


167  (21) 


188  (4) 


192  (6) 


198  (4) 

Momentgenerating Functions for Continuous Random Variables 


202  (4) 

Expectations of Discontinuous Functions and Mixed Probability Distributions 


206  (5) 

Activities for Students: Simulation 


211  (7) 


218  (5) 


218  (5) 

Multivariate Probability Distributions 


223  (46) 

Bivariate and Marginal Probability Distributions 


223  (9) 

Conditional Probability Distributions 


232  (3) 

Independent Random Variables 


235  (4) 

Expected Values of Functions of Random Variables 


239  (11) 

The Multinomial Distribution 


250  (5) 

More on the Momentgenerating Function 


255  (2) 


257  (4) 

Compounding and Its Applications 


261  (1) 


262  (7) 


263  (6) 

Functions of Random Variables 


269  (33) 


269  (1) 

Method of Distribution Functions 


270  (6) 

Method of Transformations 


276  (5) 


281  (2) 

Method of Momentgenerating Functions 


283  (6) 


289  (6) 

Probabilitygenerating Functions: Applications to Random Sums of Random Variables 


295  (3) 


298  (4) 


298  (4) 

Some Approximations to Probability Distributions: Limit Theorems 


302  (25) 


302  (1) 

Convergence in Probability 


302  (4) 

Convergence in Distribution 


306  (5) 

The Central Limit Theorem 


311  (13) 

Combination of Convergence in Probability and Convergence in Distribution 


324  (1) 


325  (2) 


325  (2) 

Extended Applications of Probability 


327  (15) 


327  (3) 

Birth and Death Processes: Biological Applications 


330  (2) 

Queues: Engineering Applications 


332  (1) 

Arrival Times for the Poisson Process 


333  (1) 


334  (2) 

Renewal Theory: Reliability Applications 


336  (3) 


339  (3) 


340  (2) 
Appendix Tables 

342  (11) 
Notes on Computer Simulations 

353  (2) 
References 

355  (2) 
Answers to Selected Exercises 

357  (16) 
Index 

373  