Lecture7-2_Aug_2010

Lecture7-2_Aug_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 7-2
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UCLA EE131A (KY) 2 Known continuous rv’s: 1. Uniform rv 1. Uniform rv - A uniform rv X characterizes a random experiment with equal likely outcomes in the interval [a, b], where - < a < b < . The pdf and cdf of a uniform rv are defined and given below. a b x 1/(b-a) f(x) a b x 1 F(x)  1 , a x b, f(x) = b -a 0, x < a, b < x. 0, x < a, x - a F(x) = b, b - a 1, b < x.
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UCLA EE131A (KY) 3 Known continuous rv’s: 1. Uniform rv (2) A uniform rv, with its pdf having a constant value, characterizes a random experiment in which one has minimum knowledge of likelihood of probabilities over the interval [a, b]. A pdf and cdf of a uniform rv is easy to work with. Ex. 1. Consider the phase , as a rv taking values over the interval [- , ], of an AC voltage given by V(t) = A cos(2 t + ), - < t < . Since at any time instant t, the phase can take any value equally over the interval [- , ], then we may model it as a uniform rv with a pdf f ( ) = (1/(2 )), -  , and zero outside of [- , ].
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UCLA EE131A (KY) 4 Known continuous rv’s: 1. Uniform rv (3) Ex. 2. Suppose trains arrive at a station at 7 am, 7:15 am, and 7:30 am. A rider show up randomly (with equal prob.) over the time interval (7, 7:30) (i.e., just after
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Lecture7-2_Aug_2010 - EE 131A Probability Professor Kung...

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