131A_1_Lecture10-2_Winter_2012

131A_1_Lecture10-2_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 10-2
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UCLA EE131A (KY) 2 Jointly distribution of two rv’s (1) For a single rv X, it is fully characterized by its cdf F X (x) or the pdf f X (x). However, in many situations, we must deal two or more rv’s at any instant. Ex. 1. Consider an urn with 100 balls. The balls are colored Black or White and are numbered 1, 2, 3, or 4. Let X denote the number on the ball and Y denote the color with Y = 0 for the Black and Y = 1 for the White balls. Their distributions are given as follows: Y \ X 1234 0 (B) .12 .12 .12 .15 1 (W) .14 .13 .14 .08
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UCLA EE131A (KY) 3 Jointly distribution of two rv’s (2) Ex. 1. (Continue). Equating relative freq. to probability: Y \ X 1234 0 (B) .12 .12 .12 .15 1 (W) .14 .13 .14 .08 The joint pmf of the (Y,X) rv’s are defined by P(Y=i and X=j) = p ij , i = 0, 1; j = 1, 2, 3, 4. P(Y=0 and X=1) = p 01 = 0.12; P(Y=0 and X=3) = p 03 = 0.12; P(Y=1 and X=1) = p 11 = 0.14; P(Y=1 and X=3) = p 13 = 0.14; P(Y=0 and X=2) = p 02 = 0.12; P(Y=0 and X=4) = p 04 = 0.15; P(Y=1 and X=2) = p 12 = 0.13; P(Y=1 and X=4) = p 14 = 0.08.
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131A_1_Lecture10-2_Winter_2012 - EE 131A Probability...

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