Fall 2009 course

Course outline

• Introduction. Events and outcomes. Probability rules.
• Conditional probability. Independence. Bayes' Rule. Combinatorics.
  
• Random variables and their distributions. Discrete random variables.
• Discrete distributions: Bernoulli, Binomial, Geometric, Negative Binomial, Poisson.
  
• Continuous distributions and probability densities.
• Continuous distributions: Exponential, Gamma, Weibull, Uniform, and Normal
  
• Expectation and moments. Central Limit Theorem.
  
• Review and MIDTERM EXAM
  
• Simulation of discrete and continuous random variables (from lecture notes). Solving problems by Monte Carlo methods.
  
• Stochastic processes. Main concepts and classification. Bernoulli process. Poisson process.
  
• Markov chains and simple queuing systems. Simulation, performance evaluation.
  
• Statistical inference. Parameters and statistics.
• Parameter estimation and hypothesis testing.
• Linear regression. Method of least squares (if time permits).
  
• Review and FINAL EXAM
  
  Prerequisite: Calculus II (MATH 2419 or MATH 1326 or equivalent)

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  WebCT - check your performance and join discussion groups

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  Some Lecture Notes

  (You may need Acrobat Reader to see and print these notes)
  
  Notes 0 "Introduction to this course"
  Notes 1 "Introduction to Probability. Set operations. Basic rules of Probability"
  Notes 2 "Equally likely outcomes. Conditional probability"
  Notes 3 "Random variables and distributions"
  Notes 4 "Discrete distributions"
  Notes 5 "Continuous distributions"
  Notes 6 "Important continuous distributions"
  Notes 7 "Expectation, variance, and Central Limit Theorem"
  Table of Normal distribution (without typos)
  Notes 8 "Computer simulations and Monte Carlo methods"
  Notes 9 "Stochastic processes. Bernoulli, Binomial, Poisson processes."
  Notes 10 "Markov chains"
  Notes 11 "Single-server queuing systems"
  Notes 12 "Statistical inference"
  
  

Matlab corner

Markov chain for sunny and cloudy days
Markov chain for the game of ladder
Poisson process of arrivals
Bernoulli and Binomial processes
Brownian motion
Central Limit Theorem