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Probability and Statistics Lecture Series - Fall 2012

Gain insights into probability rules, model-building, random variables, distributions, expectations, and statistical analysis. Covering various topics like Bayes' Rule, moments, densities, joint variables, and hypothesis testing.

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Probability and Statistics Lecture Series - Fall 2012

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  1. IE 300, Fall 2012Richard SowersIESE

  2. 8/30/2012 Goals: • Rules of Probability • Counting • Equally likely • Some examples

  3. 9/4/2012 Goals • Conditional Probability • Model-building

  4. 9/6/2012 • Independence • Definition • Model-building • Examples

  5. 9/11/2012 • Bayes’ Rule • Implicit conditional probabilities • Random variables (if possible)

  6. 9/13/2012 • Discrete random variables • Examples • Uniform • Geometric • Binomial • Bernoulli • Probability mass functions • Expectations

  7. 9/27/2012 • Expectations and variances • Direct computations • Moment generating functions (not in book)

  8. 9/18/2012 • Expectations • Means • Variances • Moment generating functions • Several random variables • Binomial • Geometric • Bernoulli • Poisson • Uniform

  9. 9/20/2012 • Review

  10. 9/28/2012 • Expectations and Variances • Bernoulli • Binomial • Law of large numbers

  11. 10/2/2012 • Moment generating function • Bernoulli • Binomial • Geometric • Negative Binomial • Poisson • Begin continuous random variables

  12. 10/4/2012 • Continuous random variables • Properties of densities • Exponential random variables

  13. 10/9/2012 • Poisson connection to exponential random variables • Gaussian random variables

  14. 10/11/2012 • Gaussian random variables • Limit theorems

  15. 10/18/2012 • Joint random variables • Joint probability mass function • Conditioning • Marginals

  16. 10/23/2012 • More joint random variables • Joint probability mass function • Conditioning • Marginals

  17. 11/1/2012 • More on transformations of random variables • Joint Gaussians

  18. 11/6/2012 • Statistical analysis of data • Sample mean, sample variance, population variance • Histograms and frequency plots

  19. 11/13/2012 • Estimation of parameters • Bernoulli • Exponential • Gaussian

  20. 11/15/2012 • Hypothesis testing (9-5)

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