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UCLA
EE131A (KY)
1
EE 131A
Probability
Professor Kung Yao
Electrical Engineering Department
University of California, Los Angeles
M.S. OnLine Engineering Program
Lecture 102
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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
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.
 Spring '10
 KungYao
 Electrical Engineering

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