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131A_1_Lecture11-1_Winter_2012

# 131A_1_Lecture11-1_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 11-1

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UCLA EE131A (KY) 2 Jointly pdf and marginal pdf (1) Let F XY (x,y) be the joint cdf of the joint rv’s (X,Y), where X and Y can be continuous or discrete rv’s. The joint pdf f XY (x,y) of (X,Y) is given by Marginal pdf f X (x) of X is obtained from f XY (x,y) as Marginal pdf f Y (y) of Y is obtained from f XY (x,y) as 2 XY XY d f (x,y) = F (x,y), - < x < , - < y < . dxdy X XY - f (x) = f (x,y) dy , - < x < . Y XY - f (y) = f (x,y) dx , - < y < .
UCLA EE131A (KY) 3 Jointly pdf and marginal pdf (2) Ex. 1. (Ex. 2, p. 10, Lec10-2). Then XY 1, 0 x 1, 0 1, f (x,y) = 0, elsewhere . y 1 X XY X - 0 1 Y XY Y - 0 2 XY XY d f (x) = f (x,y) dy = 1 dy = 1 = F (x), 0 x < 1. dx d f (y) = f (x,y) dx = 1 dx = 1 = F (y), 0 y < 1. dy 1, 0 x < 1, 0 y < 1, d f (x,y) = F (x,y) = 0, elsesher dxdy e.

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