Sheldon Ross

First Course in Probability

  1. Combinatorial Analysis
  1. Axioms of Probability
  1. Conditional Probability and Independence
  1. Random Variables
  1. Continuous R.V
  1. Jointly Distributed R.V
  1. Properties of Expectation
  1. Limit Theorems
  1. Simulation

Common Distributions

Introduction to Probability Models

  1. Introduction to Probability
  1. R.V
  1. Conditional Probabilities
  1. Markov Chains
  1. Exponential Distributions
  1. Continuous-Time Markov Chains
  1. Renewal Theory and its Applications
  1. Queueing theory
  1. Reliability Theory
  1. Brownian Motion and Stationary Processes

Simulation

Stochastic Processes

  1. Preliminaries
  1. Poisson Process
  1. Renewal Theory
  1. Markov Chain
  1. Continuous-Time Markov Chains
  1. Martingales
  1. Random Walks
  1. Brownian Motion and Other Markov Processes
  1. Stochastic Order Relations
  1. Poisson Approximations

1.2 Basic Principle of Counting

1.3 Permutations

1.4 Combinations

1.5 Multinomial Coefficients

1.6 Number integer solutions of equations

2.2 Sample space and events

2.3 Axioms of Probability

2.4 Simple Propositions

2.5 Equally likely outcomes

2.6 Probability as a continuous set function

3.2 Conditional Probabilities

3.3 Bayes' Formula

3.4 Independent Events

3.5 P(*|F) as a Probability

4.2 Discrete r.v

4.3 E(X)

4.4 expectation of a function of a random variable

4.5 Variance

4.6 Bernoulli and Binomial R.V

4.7 Poisson R.V

4.8 Other Discrete Probability Distributions

4.9 Expected value sums of r.v

4.10 Properties of the cumulative distribution function