syllabus-ECEN303 - ECEN 303 Random Signals and Systems Fall...

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ECEN 303: Random Signals and Systems Fall 2009 Instructor: Dr. Jean-Franc ¸ois Chamberland Assistant Professor Department of Electrical and Computer Engineering Office: Room 244F, WERC Email: [email protected] (Subject: ECEN 303) Phone: (979) 845-6204 Web: http://www.ece.tamu.edu/˜chmbrlnd/Courses/ Office Hours: Monday, 3:00–4:30 p.m. Course Outline This course will introduce the student to the fundamental concepts of probability theory applied to engi- neering problems. Its objective is to develop the ability to construct and exploit probabilistic models in a manner that combines intuition and mathematical precision. The proposed treatment of probability includes elementary set operations, sample spaces and probability laws, conditional probability, independence, and notions of combinatorics. A discussion of discrete and continuous random variables, common distributions, functions and expectations forms an important part of this course. Transform methods, limit theorems, con- vergences and bounding techniques are also covered. In particular, special consideration is given to the law of large numbers and the central limit theorem. Many examples from engineering, science, and statistics will be provided. Major Goals 1. Review basic notions of set theory and simple operations such as unions, intersections, differences and De Morgan’s laws. Discuss cartesian products and simple combinatorics. Go over the counting principle, permutations, combinations and partitions. 2. Introduce sample spaces, probability laws and random variables. Distinguish between events and outcomes, and illustrate how to compute their probabilities. 3. Present the concepts of independence and conditional probabilities. Study the total probability the- orem and Bayes’ rule. Provide examples of these important results applied to tangible engineering problems. 4. Understand mathematical descriptions of random variables including probability mass functions, cu- mulative distribution functions and probability density functions. Become familiar with commonly encountered random variables, in particular the Gaussian random variable. 5. Introduce the notions of expectations and moments, including means and variances. Calculate mo- ments of common random variables. Characterize the distributions of functions of random variables.
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6. Explore the properties of multiple random variables using joint probability mass functions and joint probability density functions. Understand correlation, covariance and the correlation coefficient. Dis- cuss how these quantities relate to the independence of random variables.
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