V.  OUTLINE

1. Introduction
   1. Course requirements
   2. Grading
   
   
2. Historical overview

3. Probability
   1. Definition
   2. Counting rules
   3. Conditional probability
   4. Odds
   
   
4. Discrete Probability Distributions
   1. Random variables
   2. Expectation
   3. Distributions
      1. Bernoulli
      2. Binomial
      3. Geometric
      4. Negative Binomial
      5. Poisson
      6. Hypergeometric
   4. Moment-generating functions
   5. Markov chains
   
   
5. Continuous Probabilty Distributions
   1. Random variables
   2. Expectation
   3. Distributions
      1. Uniform
      2. Exponential
      3. Gamma
      4. Normal
      5. Beta
      6. Weibull
   4. Reliability
   5. Moment-generating functions
   6. Discontinuous functions
   
   
6. Multivariate Probability Distributions
   1. Bivariate
   2. Conditional
   3. Random variables
   4. Expectation
   5. Multinomial distribution
   6. Moment-generating functions
   7. Conditional expectations
   
   
7. Functions of Random Variables
   1. Distribution functions
   2. Transformations
   3. Conditioning
   4. Moment-generating functions
   
   
8. Approximations
   1. Convergence
   2. Central Limit Theorem
   
   
9. Applications
   1. Poisson process
   2. Birth and death processes
   3. Queues