Lecture7-1_Aug_2010

Lecture7-1_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 7-1
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UCLA EE131A (KY) 2 Known discrete rv’s: 1. Bernoulli rv 1. Bernoulli rv - A Bernoulli rv X characterize a random experiment with two possible outcomes labeled as a “success” or a “failure”, with X = 1 for a “success” and X = 0 for a “failure”. Denote P(X = 1) = p(1) = p, P(X = 0) = p(0) = 1 – p = q. Ex. 1. Our previously encountered random experiments of tossing of a coin yields a Bernoulli rv. Ex. 2. The labels of a “success” or a “failure” has no probabilistic significance. We could have used labels of a “head” or a “tail”. The only relevant information is the probabilities of p and q = 1- p.
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UCLA EE131A (KY) 3 Known discrete rv’s: 2. Binomial rv (1) 2. Binomial rv – Consider n independent trials, each trial with two possible outcomes; one labeled as a “success” with probability p and the other labeled as a “failure” with probability q. Let X represent the number of successes in n Bernoulli trials . Then X is a binomial rv with the parameters of (n, p). The probability that X = i, is denoted by In (*), any specific realization of i successes and (n-i) failures is p i (1-p) n-i . Combination of such realizations is given by in - i n P(X=i)=p(i)= p (1-p) , i = 0, , n. (*) i    n i n i n! C = . (n-i)! i!
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UCLA EE131A (KY) 4 Known discrete rv’s: 2. Binomial rv (2) The probability p(i) of (*) in the last page is called a probability mass function (pmf).
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This note was uploaded on 11/05/2010 for the course ELECTRICAL EE131A taught by Professor Kungyao during the Spring '10 term at UCLA.

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Lecture7-1_Aug_2010 - EE 131A Probability Professor Kung...

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