Introduction to Probability, by D.P. Bertsekas and J.N. Tsitsiklis. Supplemental
reading ... Probability and Stochastic Processes, by R.D. Yates and D.J.
Goodman.
EECS 126: Probability and Random Processes Time and Place: Lectures: TT 9:30-11, 122 Wheeler. Discussions: W 5-6pm, 285 Cory, Th 8-9am 9 Lewis. Instructor: David Tse, Room 261M, Cory, x2-5807, dtse@eecs. Office hours: 2:30-3:30 Tues. and Thurs. Teaching Assistant: Minghua Chen, minghua@eecs. Office hour: TBA Room: TBA. Administrative Assistant: Chris Colbert, Room 231 Cory, x2-8458, chrisc@eecs Description: This course covers the fundamentals of the tools of probabilistic modeling useful in a diverse range of EECS fields such as networks, communication, signal processing and control. Prerequisite: Basic knowledge of calculus and exposure to mathematical concepts such as sets, functions, etc. Evaluation: There will be weekly problem sets (20 % of the grade), two midterms (20 % each) and a final (40 %). First midterm will be in class on February 26. Texts: • Introduction to Probability, by D.P. Bertsekas and J.N. Tsitsiklis. Supplemental reading on reserve in the engineering library: • Probability and Random Processes for Electrical Engineering by Alberto LeonGarcia, 2nd Edition. • Introduction to probability models, by Sheldon M. Ross. • Probability and Stochastic Processes, by R.D. Yates and D.J. Goodman.
Course Outline: 1) Introduction: Why probability models? Sources of randomness. Examples and application of probability models in EECS. 2) Foundations: Sample space, events, axioms of probability. Conditional probability, independence. Sequential experiments. 3) Discrete Random variables: Definition. Probability mass functions. Functions of random variables. Expectations. Joint probability mass functions of multiple random variables. Conditional distribution. Independent random variables. Important distributions. 4) General random variables: Continuous random variables. Cumulative distribution function, probability density function. Important distributions. Expectations, covariances. Conditioning. Simulation of random variables. 5) Further topics on random variables: Moment generating functions. Sums of random variables. Conditional expectation. 6) Detection and estimation: Hypothesis testing. Maximum likelihood estimation. Confidence intervals. Minimum mean-square estimation. Linear least square estimation. Examples from communication and signal processing. 7) Laws of large numbers: Weak and strong law of large numbers. Central limit theorem. 8) Random processes: Bernoulli process. Poisson process. Markov chains. Concept of state. Transition probability matrix. Steady-state behavior. Time-average versus ensemble average. Communication network examples.
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