5.2.26. Bird songs can be characterized by the number of clusters of "syllables" that are strung together in rapid succession. If the last cluster is defined as a "success," it may be reasonable to treat the number of clusters in a song as a geometric random variable. Does the model Px(k) (1 - p)k-1p, k 1, 2,..., adequately de- scribe the following distribution of two hundred fifty song lengths (108)? Begin by finding the method of mo- ments estimate for p. Then calculate the set of "expected" frequencies. = = No. of Clusters/Song Frequency | 132 234567 ∞ 52 34 4 9 7 5 5 8 6 250

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5.2.26. Bird songs can be characterized by the number of
clusters of "syllables" that are strung together in rapid
succession. If the last cluster is defined as a "success,"
it may be reasonable to treat the number of clusters in
a song as a geometric random variable. Does the model
Px(k) (1 - p)k-1p, k 1, 2,..., adequately de-
scribe the following distribution of two hundred fifty
song lengths (108)? Begin by finding the method of mo-
ments estimate for p. Then calculate the set of "expected"
frequencies.
=
=
No. of Clusters/Song Frequency
|
132
234567 ∞
52
34
4
9
7
5
5
8
6
250
Transcribed Image Text:5.2.26. Bird songs can be characterized by the number of clusters of "syllables" that are strung together in rapid succession. If the last cluster is defined as a "success," it may be reasonable to treat the number of clusters in a song as a geometric random variable. Does the model Px(k) (1 - p)k-1p, k 1, 2,..., adequately de- scribe the following distribution of two hundred fifty song lengths (108)? Begin by finding the method of mo- ments estimate for p. Then calculate the set of "expected" frequencies. = = No. of Clusters/Song Frequency | 132 234567 ∞ 52 34 4 9 7 5 5 8 6 250
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