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131A_1_Wed_June_4_08

# 131A_1_Wed_June_4_08 - 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 Lecture Wed. June 4, 2008

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UCLA EE131A (KY) 2 Verifying an empirical pdf (1) We have studied analytical expressions of pdfs of various continuous rv’s and pmf’s of discrete rv’s. From an observed rv data, how do we accept/ reject a proposed pdf/pmf for modeling the empirical pdf? To use the Chi-Square Test for this purpose, we need to define the Chi-Square rv and its pdf. Let {X 1 , X 2 , …, X n } be n iid Gaussian rv’s of zero mean and unit variance. Then Y = S 2 (n) = X 1 2 + X 2 2 + … + X n 2 , (1) is called a Chi-Square rv with a pdf defined by f Y (y) = (y (n-2)/2 e -y/2 )/(2 n/2 Γ (n/2)), 0 < y < , (2)