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View Full Document CS70: Satish Rao: Lecture 27.
1.
Chebyshev’s inequality. (Markov’s inequality.
2.
Polling.
Variance!
What is it good for?!?
Absolutely.
.. something!
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View Full Document What do we want to bound?
Recall the number of servers problem?
Average request rate: 4
X
 number of requests.
Number of servers: 10 will be enough with prob.
.
997
.
That is,
Pr
[
X
>
10
]
< .
003
.
Pr
[
X
=
i
] = (
e

4
)
4
i
i
!
E
[
X
] =
4
λ
=
4
0
1
2
3
4
5
6
7
8
9
10
0
.
1
.
2
Plotting
Pr
[
X
>
α
]
Pr
[
X
≥
i
]
0
1
2
3
4
5
6
7
8
9
10
0
.
5
1
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View Full Document Average request rate: 100
X
 number of requests.
Number of servers: 130 will be enough with prob.
≥
135
.
That is,
Pr
[

X

100

>
30
]
< .
01
Pr
[
X
≥
i
]
λ
=
100
0
15
30
45
60
75
90
105
120
135
150
0
.
5
1
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View Full Document Bound
Pr
[

X

μ

>
α
]
!
Chebyshev’s Inequality:
For a random variable
X
with
expectation
μ
Pr
[

X

μ
 ≥
α
]
≤
Var
(
X
)
α
2
.
Corollary:
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This note was uploaded on 02/29/2012 for the course COMPSCI 70 taught by Professor Rau during the Fall '11 term at University of California, Berkeley.
 Fall '11
 Rau

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