An otherwise fair six-sided die has been tampered with in an attempt to cheat at a dice game. The effect is that the 1 and 6 faces have a different probability of occurring than the 2, 3, 4 and 5 faces. Let 0 be the probability of obtaining a 1 on this biased die. Then the outcomes of rolling the biased die have the following probability mass function.
An otherwise fair six-sided die has been tampered with in an attempt to cheat at a dice game. The effect is that the 1 and 6 faces have a different probability of occurring than the 2, 3, 4 and 5 faces. Let 0 be the probability of obtaining a 1 on this biased die. Then the outcomes of rolling the biased die have the following probability mass function.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Related questions
Question
![An otherwise fair six-sided die has been tampered with in an attempt to
cheat at a dice game. The effect is that the 1 and 6 faces have a
different probability of occurring than the 2, 3, 4 and 5 faces.
Let 0 be the probability of obtaining a 1 on this biased die. Then the
outcomes of rolling the biased die have the following probability mass
function.
Table 1 The p.m.f. of outcomes of rolls of a biased die
Outcome
3
6.
Probability 0 1(1– 20) |(1- 20) ļ0– 20) |(1– 20) 0
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 cach
of n= 331 wood mice were caught in a particular trap (over a two-year
time period).
Table 3
Numbers of trappings of wood mice
Times trapped
Frequency
3 4
20
9.
71
59 41 39
26
19
12
9.
Times trapped 10
Frequency
11
12
13
14
15
16
17 18
8 4 9 2
3
3
3
Question 1:
What is the value of the maximum likelihood estimate, 0, of 0
based on these data? Justify your answer. What does the value of
suggest about the value of 0 for this biased die compared with the
value of 0 associated with a fair, unbiased, die?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc0557e0e-7c52-43d2-b9f4-a887bc43498a%2Fcefea75e-8f03-42f0-aedf-7cd765b40b8a%2Fqw32u4w_processed.jpeg&w=3840&q=75)
Transcribed Image Text:An otherwise fair six-sided die has been tampered with in an attempt to
cheat at a dice game. The effect is that the 1 and 6 faces have a
different probability of occurring than the 2, 3, 4 and 5 faces.
Let 0 be the probability of obtaining a 1 on this biased die. Then the
outcomes of rolling the biased die have the following probability mass
function.
Table 1 The p.m.f. of outcomes of rolls of a biased die
Outcome
3
6.
Probability 0 1(1– 20) |(1- 20) ļ0– 20) |(1– 20) 0
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 cach
of n= 331 wood mice were caught in a particular trap (over a two-year
time period).
Table 3
Numbers of trappings of wood mice
Times trapped
Frequency
3 4
20
9.
71
59 41 39
26
19
12
9.
Times trapped 10
Frequency
11
12
13
14
15
16
17 18
8 4 9 2
3
3
3
Question 1:
What is the value of the maximum likelihood estimate, 0, of 0
based on these data? Justify your answer. What does the value of
suggest about the value of 0 for this biased die compared with the
value of 0 associated with a fair, unbiased, die?
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