131A_1_Lecture15-2_Winter_2012

131A_1_Lecture15-2_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 15-2
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UCLA EE131A (KY) 2 Background materials for class project The purpose of this project is to study the analytical and Monte Carlo simulation properties of a Gaussian sequence (denoted as Class A) and a mixture of two independent Gaussian sequences (denoted as Class B). Case A Here the random sequence {N(k) , k = 1, …, n}, is a sequence of length n independent rv’s each having a zero mean Gaussian rv of standard deviation = 1. The Gaussian pdf f(x) = (2 ) -0.5 exp(-x 2 /2), - < x < , has the Matlab function normpdf(x, 0, 1) representation. The Gaussian cdf F(x) = (x) = 1 – Q(x), has the Matlab function normcdf(x, 0, 1) representation.
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UCLA EE131A (KY) 3 Case B Now, consider the mixture of two zero mean independent Gaussian random sequences modeled by N(k) = 0.4 N 1 (k) + 0.6 N 2 (k), k = 1, …, n , where the standard deviations are
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131A_1_Lecture15-2_Winter_2012 - EE 131A Probability...

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