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Random Variable
Random Variable
X
is a mapping that maps each outcome
s
in the sample space to a unique
real number
x
,
x
−∞ <
< ∞
.
You must specify how the mapping
X
operates.
” Let
X
be the random variable indicating the number of packets waiting ….”
”
X
is a binary random variable.
X=1
if the outcome satisfies …”
Sometimes the outcome itself is a real number. In that case,
X
simply shows the outcome.
REAL LINE
s
x
()
Xs x
=
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View Full Document Example Bernoulli
Toss a biased coin which shows head with probability p.
Define random variable
X
as
1
0
if the outcome is a head
X
otherwise
=
Mapping Terminology
Range (of the random variable
X
)
{:
()
}
X
S
x x
X s for some s
S
=
=
∈
In general,
X
is a manytoone mapping.
Inverse Operation
1
Xx
−
: for any
X
xS
∈
,
1
() {: ()
}
X x
s Xs x
−
=
Inverse Image
1
XJ
−
: for any
X
JS
⊂
,
1
( ) {: ()
}
X J
s Xs J
−
=
We make use of the fact that
1
[
]
[{ :
( )}]
PX J
P s s X
J
−
∈=
∈
REAL LINE
s
x
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View Full Document Example Bernoulli
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This note was uploaded on 11/23/2010 for the course EE EE528 taught by Professor Majungsoo during the Spring '10 term at Korea Advanced Institute of Science and Technology.
 Spring '10
 Majungsoo

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