Lecture_1-1_July_2010

Lecture_1-1_July_2010 - EE 131A Probability Professor Kung...

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UCLA EE131A (KY) 1 EE 131A Probability Professor Kung Yao Electrical Engineering Department University of California, Los Angeles M.S. On-Line Engineering Program Lecture 1-1
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UCLA EE131A (KY) 2 Importance of Probability All modern information processing systems are designed and analyzed using probabilistic concepts It is crucial to understand probability in order to study all aspects of communication, telecommunication, comm/computer networks, multimedia/image/signal processing, radar/avionic systems, etc. It is the purpose of this course to teach the theory as well as the computational aspects of probability, random processes, and statistical methods for system applications
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UCLA EE131A (KY) 3 Some Motivational Probability Examples a. Consider a low-cost manuf. item (e.g. car battery guaranteed for 60 months). Based on materials & manuf. process, suppose the probability item meets spec = 0.9999 (i.e., 1 defect in 10,000) b. Consider a high-quality manuf. item (e.g. CPU guaranteed for 10 years) based on the 6-sigma quality criterion with a probability item meets spec = 0.9999966 (i.e., 34 defects in 10 8 ) 0 10 years time Probability = 0.9999966 Case b 0 60 months time Probability = 0.9999 Case a
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UCLA EE131A (KY) 4 “Black Swan” or “Fat-Tail” Probability Events (1) The above used 6-sigma criterion (commonly used in high quality manufacturing) based on the use of “Central Limit Theorem” (CLT) assumption (i.e., sum of large number of independent events results in a Gaussian random variable) Most modeling of random noises in free-space propagation assumes Gaussian random variables However, some complicated physical phenomena (e.g. multipath radio fadings) and economic systems need not behave with the simple CLT assumption as shown on the next slide
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UCLA EE131A (KY) 5 “Black Swan” or “Fat-Tail” Probability Events (2) Suppose the GNP is modeled by a Gaussian prob. den. (due to CLT). At the nominal operating pt, some unexpected disaster happens with very low prob. But suppose GNP actually has a “fat-tail” prob. den. At the same operating pt., some unexpected disaster (called a “black swan” event) happens much more often than expected from the CLT model (e.g., 1988 LTCM crash; 2002 Internet bubble; 2007-2008 crash) Same operating point Gaussian prob. density (CLT) = 1 6    6 “Fat-tail prob. density Probability = 0.9999966 Probability = 0.95 Probability = 0.0000034 Probability = 0.05
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UCLA EE131A (KY) 6 “Black Swan” or “Fat-Tail” Probability Events (3)
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This note was uploaded on 10/27/2010 for the course EE 131A 190-625-28 taught by Professor Kungyao during the Fall '10 term at UCLA.

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Lecture_1-1_July_2010 - EE 131A Probability Professor Kung...

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