All of this reading is from the ninth edition of Introduction to Probability Models by Sheldon Ross.

• Review of Basic Probability
  • Conditional Probability
  • Exponential and Gamma Distributions
• Markov Chains
  • Introductory Examples
  • The Chapman-Kolmogorov Equations
  • Classification of States
  • Limiting Probabilities
  • The Gambler's Ruin Problem
  • The Binomial Pricing Model for Stocks
  • Mean Time in Transient States
  • Branching Processes
• Poisson Process
  • The Waiting Time Approach to the Poisson Process
  • The Differential Equation Approach to the Poisson Process
  • Poisson Random Sums and Insurance Claims
  • Non-homogeneous Poisson Processes
  • A Model of Software Reliability
• Continuous Time Markov Chains
  • Some Finite State Examples
  • The Waiting Time Approach to Continuous Time Markov Chains
  • The Differential Equation Approach to Continuous Time Markov Chains
  • Birth and Death Processes
  • Some Simple Queing Models
• Brownian Motion and Martingales
  • Introduction to Brownian Motion
  • The Gambler's Ruin Problem for Brownian Motion
  • Geometric Brownian Motion
  • A Simple Stochastic Differential Equation and Ito's Lemma
  • Pricing Stock Options with Geometric Brownian Motion: The Black-Scholes Formula.
• Simulation
  • Three General Methods of Simulating IID Sequences of Random Variables.
  • Applications to Well-Known Distributions