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 p X ( k ) = ( 1 − p ) k − 1 p , k = 1 , 2 , ... , adequately describe the following distribution of two hundred fifty song lengths ( 108 ) ? Begin by finding the method of moments estimate for p . Then calculate the set of “expected” frequencies. No. of Clusters/Song Frequency 1 132 2 52 3 34 4 9 5 7 6 5 7 5 8 6 250 ¯
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 p X ( k ) = ( 1 − p ) k − 1 p , k = 1 , 2 , ... , adequately describe the following distribution of two hundred fifty song lengths ( 108 ) ? Begin by finding the method of moments estimate for p . Then calculate the set of “expected” frequencies. No. of Clusters/Song Frequency 1 132 2 52 3 34 4 9 5 7 6 5 7 5 8 6 250 ¯
Solution Summary: The author explains the method of moments estimate for p. Bird songs can be characterized by the number of clusters of "syllabus" that are strung together in rapid succession.
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
p
X
(
k
)
=
(
1
−
p
)
k
−
1
p
,
k
=
1
,
2
,
...
,
adequately describe the following distribution of two hundred fifty song lengths
(
108
)
? Begin by finding the method of moments estimate for
p
. Then calculate the set of “expected” frequencies.
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