Fundamentals of Probability: With Stochastic Processes, Third Edition (Hardcover, 3)

Axioms of Probability
Introduction
Sample Space and Events
Axioms of Probability
Basic Theorems
Continuity of Probability Function
Probabilities 0 and 1
Random Selection of Points from Intervals
Review Problems

Combinatorial Methods
Introduction
Counting Principle
Permutations
Combinations
Stirling’s Formula
Review Problems

Conditional Probability and Independence
Conditional Probability
Law of Multiplication
Law of Total Probability
Bayes’ Formula
Independence
Applications of Probability to Genetics
Review Problems

Distribution Functions and Discrete Random Variables
Random Variables
Distribution Functions
Discrete Random Variables
Expectations of Discrete Random Variables
Variances and Moments of Discrete Random Variables
Standardized Random Variables
Review Problems

Special Discrete Distributions
Bernoulli and Binomial Random Variables
Poisson Random Variable
Other Discrete Random Variables
Review Problems

Continuous Random Variables
Probability Density Functions
Density Function of a Function of a Random Variable
Expectations and Variances
Review Problems

Special Continuous Distributions
Uniform Random Variable
Normal Random Variable
Exponential Random Variables
Gamma Distribution
Beta Distribution
Survival Analysis and Hazard Function
Review Problems

Bivariate Distributions
Joint Distribution of Two Random Variables
Independent Random Variables
Conditional Distributions
Transformations of Two Random Variables
Review Problems

Multivariate Distributions
Joint Distribution of n > 2 Random Variables
Order Statistics
Multinomial Distributions
Review Problems

More Expectations and Variances
Expected Values of Sums of Random Variables
Covariance
Correlation
Conditioning on Random Variables
Bivariate Normal Distribution
Review Problems

Sums of Independent Random Variables and Limit Theorems
Moment-Generating Functions
Sums of Independent Random Variables
Markov and Chebyshev Inequalities
Laws of Large Numbers
Central Limit Theorem
Review Problems

Stochastic Processes
Introduction
More on Poisson Processes
Markov Chains
Continuous-Time Markov Chains
Brownian Motion
Review Problems

Simulation
Introduction
Simulation of Combinatorial Problems
Simulation of Conditional Probabilities
Simulation of Random Variables
Monte Carlo Method