Lecture10-2_Oct_2010

Lecture10-2_Oct_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 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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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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Lecture10-2_Oct_2010 - EE 131A Probability Professor Kung...

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