# Courses

## EE 126. Probability in Electrical Engineering and Computer Science

### Current Schedule (Spring 2014)

- EE 126: Jean Walrand, TuTh 930-11A, 285 Cory [course homepage]

### Description

Updated Description: (4 units) Three hours of lecture and one hour of discussion per week. This course explains applications of probability in electrical engineering and computer sciences: PageRank, Multiplexing, Digital Link, Tracking, Speech Recognition, Route Planning and more. Topics include Markov chains, detection, coding, estimation, Viterbi algorithm, expectation maximization, clustering, compressed sensing, recommender systems, Kalman Filter, Markov decision problems, LQG, and channel capacity. Matlab examples are used to simulate models and to implement the algorithms. The necessary concepts from basic probability and linear algebra are reviewed.

Prerequisites: CS 70.

Course objectives: This course introduces probability and probalistic models. The objective is to equip students with the basic tools required to build and analyze such models in both the discrete and continuous context.

Topics Covered:

- Basic probability: probability space, random variables, expectation of functions, change of density.
- PageRank: balance equations, Markov chains, first step equations, convergence, law of large numbers.
- Multiplexing: central limit theorem, confidence intervals.
- Digital links: detection, MAP, MLE, Huffman and LDPC codes.
- Tracking: estimation, LLSE, MMSE, Kalman Filter.
- Speech Recognition: Viterbi algorithm, clustering and expectation maximization, matching pursuit, compressed sensing, recommender systems.
- Route Planning: Markov decision problems, LQG control.
- Complements: Poisson process, continuous and infinite Markov chains, and more.