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Material Type: Notes; Professor: Maier; Class: TOP: INTRO TO MULTIMEDIA NTWRK; Subject: Computer Science; University: Portland State University; Term: Summer 2007;
Typology: Study notes
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Data Streams: Lecture 13
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Data Streams: Lecture 13
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Data Streams: Lecture 13
n k
( )
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Data Streams: Lecture 13
( )
k
n-k
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Data Streams: Lecture 13
Binomial Distribution (n=20, q=1/3)
0
0.080.060.040.
0.180.160.140.
0
2
4
6
8
10
12
14
16
18
20
Probability
Sample Size
Expected Sample Size = 20*1/
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Data Streams: Lecture 13
8
Bernoulli Sampling - Implementation
1
2
3
i
i
i
e
1
e
2
e
6
e
5
e
4
e
3
1
2
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e
7
7
Example q = 0.
Sample:
e
2
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5
e
7
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Data Streams: Lecture 13
Geometric Distribution
q = 0.
0
0
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20
Probability
Number of Skips (
i
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Data Streams: Lecture 13
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Data Streams: Lecture 13
i
i
i
i
i
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Data Streams: Lecture 13
Sample size 3
(k=3)
Recall: p
i
= 1 i
k, p
i
= i/k i>k
e
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p
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p
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p
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e
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p
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e
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p
8
p
1
p
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p
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5
Reservoir Sample:
e
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e
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e
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e
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e
5
e
8
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Data Streams: Lecture 13
Reservoir Sampling - Observations
i
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Data Streams: Lecture 13
th
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Data Streams: Lecture 13
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Data Streams: Lecture 13
Deterministic Semi-deterministicSchemes
e
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n=18, k=