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Independent Events
Two events,
A
and
B
, are independent, if
P
(
A
∩
B
) =
P
(
A
)
P
(
B
)
,
or, equivalently, if
P
(
A

B
) =
P
(
A
)
as long as
P
(
B
)
6
= 0.
If
P
(
B
) = 0 then
A
and
B
are always indepen
dent.
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View Full Document Independence of more than 2 events
3 events
Events
A
1
,
A
2
and
A
3
are called
independent if
P
(
A
1
∩
A
2
) =
P
(
A
1
)
P
(
A
2
)
,
P
(
A
1
∩
A
3
) =
P
(
A
1
)
P
(
A
3
)
,
P
(
A
2
∩
A
3
) =
P
(
A
2
)
P
(
A
3
)
,
P
(
A
1
∩
A
2
∩
A
3
) =
P
(
A
1
)
P
(
A
2
)
P
(
A
3
)
.
If only the ﬁrst 3 requirements hold, then the
events are called
pairwise independent
.
There are examples of pairwise independent
events that are NOT independent.
Independence of
n
events
Events
A
1
,A
2
,...,A
n
are called independent if
for any selection
A
i
1
,A
i
2
,...,A
i
k
of these events
P
(
A
i
1
∩
A
i
2
∩
...
∩
A
i
k
) =
P
(
A
i
1
)
P
(
A
i
2
)
...P
(
A
i
k
)
for
k
= 2
,
3
,...,n
.
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View Full Document An equivalent deﬁnition is given in the text
:
Events
A
1
,A
2
,...,A
n
are independent if
P
(
A
1
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This note was uploaded on 09/20/2010 for the course OR&IE 3500 at Cornell University (Engineering School).
 '10
 SAMORODNITSKY

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