Studies of the size and range of wild animal populations often involve tagging observed individual animals and recording how many times each is caught in a trap (from which it is then released back into the wild). The dataset presented in Table 3 consists of the numbers of times each of n = 334 wood mice were caught in a particular trap (over a two-year time period). The data are also provided in the Minitab file wood-mice.mwx.

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Studies of the size and range of wild animal populations often involve
tagging observed individual animals and recording how many times each
is caught in a trap (from which it is then released back into the wild).
The dataset presented in Table 3 consists of the numbers of times each
of n = 334 wood mice were caught in a particular trap (over a two-year
time period). The data are also provided in the Minitab file
wood-mice.mwx.
Table 3 Numbers of trappings of wood mice
Times trapped 1 2
Frequency
3 4 5 6 7 8 9
71 59 41 39 20 26 19 12
9
Times trapped 10 11 12 13 14
Frequency
5
15 16
17 18
8 49 2 13 3 3
The geometric distribution with parameter p is a good model for these
data.
(i) What is the maximum likelihood estimator of p for a geometric
model?
(ii) What is the maximum likelihood estimate of p for the data in
Table 3? You are recommended to use Minitab to help you to
answer this part of the question.
Transcribed Image Text:Studies of the size and range of wild animal populations often involve tagging observed individual animals and recording how many times each is caught in a trap (from which it is then released back into the wild). The dataset presented in Table 3 consists of the numbers of times each of n = 334 wood mice were caught in a particular trap (over a two-year time period). The data are also provided in the Minitab file wood-mice.mwx. Table 3 Numbers of trappings of wood mice Times trapped 1 2 Frequency 3 4 5 6 7 8 9 71 59 41 39 20 26 19 12 9 Times trapped 10 11 12 13 14 Frequency 5 15 16 17 18 8 49 2 13 3 3 The geometric distribution with parameter p is a good model for these data. (i) What is the maximum likelihood estimator of p for a geometric model? (ii) What is the maximum likelihood estimate of p for the data in Table 3? You are recommended to use Minitab to help you to answer this part of the question.
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