CNS 286, Spring 2008
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CNS 286C - Course Syllabus (Spring 2008)

Date	Topics (90-Minute lectures)	Lecture Notes and Reading
Week #1: Mar. 31 - Apr. 4	A. Organization of Course B. Introduction and Mathematical Background: The Basic Terminology of Probability Theory Sample Spaces Probability Measures C. Permutations and Combinations: Binomial Coefficients The Matching Problem The Birthday Problem The Girl-Named-Florida Problem D. Intro to Conditional Probability: Definition of Conditional Probability Relations between Intersections and Conditional Probability Inverse Probability Conditioning Bayes' Rule	Lecture 1 Notes Lecture 2 Notes Lecture 3 Notes
Week #2: Apr. 7 - Apr. 11	More Conditional Probability: Medical Screening Tests Neuronal Sparseness Model Prior and Posterior Probability Bayesian Updating Tree Diagrams The Monty Hall Problem Independence B. Introduction to Random Variables: Set Functions Concept of a random variable Discrete Random Variables Continuous Random Variables The Definition of Continuity Probability Distributions and Densities Cumulative Distribution Functions	Lecture 4 Notes Lecture 5 Notes Lecture 6 Notes
Week #3: Apr. 14 - Apr. 18	More Random Variables: Changes of Variable Joint and Marginal Distributions Expectations: Expectation of a Random Variable Expectations of Sums Bernoulli trials Indicator Variables Expectations in Occupancy Problems Solving Matching Problems Employing Indicator Variables The Coupon Collector's Problem Expectations of Products Intro to Moments Moments of Probability Distributions Moment Generating Functions The Second Moment and the Variance Linear Transformations of a Random Variable	Lecture 7/8 Notes
Week #4: Apr. 21 - Apr. 25	More on Moments: The Covariance of Two Random Variables The Probability Density for a sum of Random Variables The Variance in Matching Problems Special Probability Distributions: The Discrete and Continuous Uniform Distribution A Gambler's Paradox The Binomial Distribution The Relation of Binomial Distribution and Bernoulli Trials The Poisson Approximation to the Binomial Distribution The Poisson Distribution and Applications The Geometric Distribution and Applications Intro to The Normal Distribution: Moments of Probability Distributions The Gaussian (normal) density The Normal Cumulative Distribution Function The Standard Normal Density and Distribution Function	Lecture notes will no longer be posted; copies will be available in class and from the professor directly.
Week #5: Apr. 28 - May 2	More on the Normal Distribution: Percentiles The Normal Moment Generating Function Applications to Waiting Times, Inventory Management, and Electronic Noise. The Chi Square as the Distribution for the Sum of Squared Normal Random Variables Properties of the Chi Square Distribution The Weak and strong law of large numbers The Central Limit Theorem Application to Risk in Insurance and Civil Engineering The Normal Approximation to the Binomial Distribution B. Intro to Statistical Sampling: Defining a random sample from a distribution of a random variable Inference Problems What is meant by a Statistic The Sample Mean and its Expectation The Probability Distribution of the Sample Mean
Week #6: May 5 - May 9	More Statistical Sampling: The Median and its Distribution, Expectation and Variance The Sample Variance and its Expectation Using the Normal Curve Intro to signal detection theory Relating Mean and Variance of Sample Means and Sample Variances to the Population Distribution of the Sample Mean and Variance for Normal Populations The t-distribution Some Applications Sampling from a finite population Application to Polling Data
Week #7: May 12 - May 16	Point Estimation: Biased and Unbiased Estimators Minimum Variance Estimators Consistent Estimators Point estimation Method of Maximum Liklihood Applications to Normal, Binomial and Poisson Distributions QUIZ #1 on weeks 1-5 (probability) Interval Estimation: Interval estimation Confidence Intervals Interval Estimates for a Normal Population Comparing Normal Populations Confidence Intervals for Bernoulli Random Variables Bayesian Intervals
Week #8: May 19 - May 23	Hypothesis Testing Idea Behind Hypothesis testing Losses, Errors and Risks Null and Alternative hypotheses Simple and Composite Hypotheses Significance Levels for means and variance The F-test Power of a test Likelihood ratio Type I and II errors Testing and Comparing Normal Populations Case of Unknown Variance: The t-test Analysis of variance (ANOVA) Regression and Correlation: Dependent and Independent Variables Linear Regression The Method of Least Squares Distribution of the Estimators Statistical Inferences about the Regression Parameters Regression to the Mean The Correlation Coefficient Intro to Random Processes What is a random process? Definition and Tests for Random Numbers and Sequences Coin Tossing Models Changes in leads Hot hand fallacies
Week #9: May 26 - May 30	Mon May 26 = No Class - Memorial Day Wed May 28 = QUIZ #2 on weeks 6-8 (statistics). Introduction to Random Processes Poisson processes Applications of Poisson processes Definition of Markov Processes Basic Concepts of random walks Multi-dimensional Walks Random Walks with Barriers The Ballot theorem Probability of return Last visit and long leads First passages Classic ruin problem Expected durations Brownian Motion Diffusion JUNE 6: Final Exam