Analysis: Chernoff Bound
l
Random variables
X
i
Î
[0,1]
l
Sum
X
=
å
X
i
l
Bound deviation from expectation
Pr
[
|
X
-
E
[
X
]
|
³
e
E
[
X
]
]
<
exp(-
e
2
E
[
X
]
/
4)
l
“Probably,
X
Î
(
1±
e
)
E
[
X
]
”
l
If
E[
X
]
³
4(ln
n
)
/
e
2
, “tight concentration”
»
Deviation by
e
probability
<
1
/
n