131A_1_Lecture_6-1_Winter_2012

131A_1_Lecture_6-1_Winter_2012 - EE 131A Probability...

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UCLA EE131A (KY) 1 EE 131A Probability Professor Kung Yao Electrical Engineering Department University of California, Los Angeles Lecture 6-1
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UCLA EE131A (KY) 2 Random Variable (1) So far, we have dealt with elementary outcomes and collection of elementary outcomes called events. These outcomes may be called “head,” tail,” “5 on a die,” etc. In science and engineering, for preciseness, we prefer to characterize the events in terms of numbers and not features like “head,” “tail,” “green,” etc. A random variable (rv) X is a real-valued function defined on the sample space S that yields a real number X(s) for every outcome s S .
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UCLA EE131A (KY) 3 Random Variable (2) The random variable X(s) maps each s S to a real- valued number on the real-line as shown below. 0 s 4 s 1 s 5 s 2 s 3 Sample space S Real-line X(s ) 4 X(s ) 2 X(s ) 3 X(s ) 1 X(s ) 5
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UCLA EE131A (KY) 4 Random Variable (3) Ex. 1. Flip a coin. Original sample space S = { H , T }. Introduce a rv X(.) such that X( H ) = 1 and X( T ) = 0. The new induced sample space
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131A_1_Lecture_6-1_Winter_2012 - EE 131A Probability...

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