ECS 132: Probability & Statistical Modeling for Computer Science

Summary of Course Content

I. Univariate and Multivariate Distributions

• Probability mass, density, and cumulative distribution functions
• Parametric families of distributions
• Expected value, variance, conditional expectation
• Applications of the univariate and multivariate Central Limit Theorem
• Probabilistic inequalities

II. Sampling, Estimation and Modeling Building

• Random samples, sampling distributions of estimators
• Methods of Moments and Maximum Likelihood
• Statistical inference
• Introduction to multivariate statistical models: regression and classification problems, log-linear model, principal components analysis
• The problem of overfitting; model assessment

III. Application of Markov Models

• Markov chains
• Hidden Markov models
• Queuing models
• Markov Chain Monte Carlo

IV. Computer science and engineering applications (interspersed with the above topics throughout the course)

• Data mining
• Network protocols, analysis of Web traffic
• Computer security
• Software engineering
• Computer architecture, operating systems, distributed systems
• Bioinformatics

Illustrative Reading
Possible choices include:

• K.S. Trivedi, Probability and Statistics with Reliability, Queuing, and Computer Science Applications, Wiley, New York, 2001;
• M. Mitzenmacher, E. Upfal, Probability and Computing: Randomized Algorithms and Probabilistic Analysis, Cambridge, 2005;
• N. Matloff, A Course in Probabilistic and Statistical Modeling in Computer Science http://heather.cs.ucdavis.edu/~matloff/132/PLN

Potential Course Overlap
There is some topical overlap with MAT 135A and STA 131ABC, as well as with application-specific probability/statistics courses such as ECI 114, EEC 161, ECN 140 and so on. This course differs greatly in its collection of topics, its usage of computers, and especially in its computer science applications.