131A_1_Lecture_5-2_Winter_2012

131A_1_Lecture_5-2_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 5-2
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UCLA EE131A (KY) 2 Binomial Probability Law (1) Consider a binary-valued experiment with outcomes called a success ( S ) or a failure ( F ). This experiment can model the flip of a coin, with a Head ( H ) associated with a success S and a Tail ( T ) associated with a failure F . Furthermore, let the probability of a H be denoted by P( H ) = P( S ) = p and the probability of a T be denoted by P( T ) = P( F ) = q = 1 – p. The sample space S = { H , T }. Ex. 1. Toss a coin three times. Assume the outcomes of the three trials are independent. What is the sample space of this experiment?
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UCLA EE131A (KY) 3 Binomial Probability Law (2) S = { HHH,HHT, HTH,THH,TTT,TTH,THT,HTT }. Since the outcomes are independent, then P( HHH ) = P( H )P( H )P( H ) = p 3 ; similarly, for the others P( HHT ) = p 2 (1 - p) = P( HTH ) = P( THH ); P( HTT ) = p(1 - p) 2 = P( THT ) = P( TTH ); P( TTT ) = (1 - p) 3 . Now, let k denote the number of Heads in three flips. P(k = 0) = P( TTT ) = (1 - p) 3 ; P(k = 1) = P( HTT ) + P( THT ) + P( TTH ) = 3p(1 - p) 2 ; P(k = 2) = P( HHT ) + P( HTH ) + P( THH ) = 3p 2 (1 - p); P(k = 3) = P( HHH ) = p 3 .
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UCLA EE131A (KY) 4 Binomial Probability Law (3) A Bernoulli trial
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This note was uploaded on 02/29/2012 for the course ELECTRICAL 131a taught by Professor Yao during the Spring '12 term at UCLA.

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131A_1_Lecture_5-2_Winter_2012 - EE 131A Probability...

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