ie 300, fall 2012 richard sowers iese. 8/30/2012 goals: rules of probability counting equally likely...

IE 300, Fall 2012Richard Sowers

IESE

8/30/2012

Goals:•Rules of Probability•Counting•Equally likely•Some examples

9/4/2012

Goals•Conditional Probability•Model-building

9/6/2012

• Independence– Definition– Model-building– Examples

9/11/2012

• Bayes’ Rule– Implicit conditional probabilities

• Random variables (if possible)

9/13/2012

• Discrete random variables– Examples

• Uniform• Geometric• Binomial• Bernoulli

– Probability mass functions• Expectations

9/27/2012

• Expectations and variances– Direct computations– Moment generating functions (not in book)

9/18/2012

• Expectations– Means– Variances– Moment generating functions

• Several random variables– Binomial– Geometric– Bernoulli– Poisson– Uniform

9/20/2012

• Review

9/28/2012

• Expectations and Variances– Bernoulli– Binomial– Law of large numbers

10/2/2012

• Moment generating function– Bernoulli– Binomial– Geometric– Negative Binomial– Poisson

• Begin continuous random variables

10/4/2012

• Continuous random variables• Properties of densities• Exponential random variables

10/9/2012

• Poisson connection to exponential random variables

• Gaussian random variables

10/11/2012

• Gaussian random variables• Limit theorems

10/18/2012

• Joint random variables• Joint probability mass function• Conditioning• Marginals

10/23/2012

• More joint random variables• Joint probability mass function• Conditioning• Marginals

11/1/2012

• More on transformations of random variables

• Joint Gaussians

11/6/2012

• Statistical analysis of data• Sample mean, sample variance, population

variance• Histograms and frequency plots

11/13/2012

• Estimation of parameters– Bernoulli– Exponential– Gaussian

11/15/2012

• Hypothesis testing (9-5)