Lect 1 - ECE4110 Lecture 27 Aug Fall 09 Cornell University...

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Unformatted text preview: ECE4110 Lecture: 27 Aug Fall 09 Cornell University T.L. Fine 1. Course Organization (1) Discuss the General Information handout with the class. (2) RH312 for “office hour” from 4pm to 5pm on Wednesdays—just prior to homeworks due on Thursday and prelims on Thursday nights. (3) Expand on Academic Integrity and consulting others , yet doing the work yourself. 2. Distinctions between Random Variables and Random Processes (1) Introductory probability is mostly about posing and answering questions involving one or a few random variables. (2) However, in the context of random signals extending over time, or more generally extending as well over other variables such as spatial coordinates, we encounter questions involving infinitely many random variables. (3) For example, “What is the maximum value of an analog signal observed over an hour?” or “What is the energy in an analog signal observed over a minute?”. (4) While in practice we might retreat from “infinitely many” to a “very large number”, this can actually make the problem much harder to understand and solve. (5) For example, “What is the probability that an analog signal will exceed a given value over a given time period?”, is a question about an uncountable number of random variables, the signal amplitudes at all times in the given time period. (6) Given this, it is evident that we will be concerned with limiting processes. (7) In probability theory, unlike the calculus you have learned, we deal with four kinds of limiting processes, and these will have to be introduced and applied. (8) For example, convergence in distribution is what the celebrated Central Limit Theorem needs and it in turn explains the ob- served prevalence of Gaussian phenomena. 1 2 (9) The theory of random [Latin] or stochastic [Greek] processes addresses such questions by providing a large number of ran- dom process models (e.g., Gaussian, Bernoull, Poisson, Markov, Martingale, Renewal) that have repeatedly proven useful in both theory and practice and about which much is known....
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Lect 1 - ECE4110 Lecture 27 Aug Fall 09 Cornell University...

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