Essentials of Probability

• Basic Definitions
• Modeling Experiments with Uncertainty
• Random Variables: Geometric, Poisson, Exponential
• Read any of the probability references, e.g. Ross, Molloy, Papoulis, Stark and Woods
• Next read Appendix A in Tanenbaum: ``Introduction to Queueing Theory" (Skip A.4.3, it's wrong). Also can read Sections 2.1-3 in Schwartz.

• Probability on a Sample Space
  • Basic Operations on Events
  • Probability on Events
  • Other Properties
• Conditional Probability
• Bayes Formula
• Independence
• Random Variables
  • Random Variable as a Measurement
  • Probability Mass Function for a Random Variable
  • Cumulative Distribution Function
    • PMF and CDF for the 3 Coin Toss Example
  • Expectation of a Random Variable
• Important Random Variables
  • Bernoulli Random Variable
  • Binomial Random Variable
  • Geometric Random Variable
  • Poisson Random Variable
• Continuous-valued Random Variables
  • Properties of Continuous Random Variables
  • Expectation of a Continuous Random Variable
  • Important Continuous Random Variable: Exponential
  • Memoryless Property of the Exponential