Document1 Layout References Mailings Review O Tell me View Z Aa fx v sine X e* 0 - h. - B9 - gral Sum Fonts Formula Fraction Function Radical Script Equation Statistical Matrix Symbols 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 4 6. Probability 0 (1 – 20) (1– 20) }(1- 20) (1- 20) 0 Table 2 Outcomes of 1000 independent rolls of a biased die Outcome 1. Frequency 205 154 141 165 145 190 Show that the likelihood of 0 based on these data is L(0) = C0395 (1 – 20)605, where C is a positive constant, not dependent on 0.
Document1 Layout References Mailings Review O Tell me View Z Aa fx v sine X e* 0 - h. - B9 - gral Sum Fonts Formula Fraction Function Radical Script Equation Statistical Matrix Symbols 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 4 6. Probability 0 (1 – 20) (1– 20) }(1- 20) (1- 20) 0 Table 2 Outcomes of 1000 independent rolls of a biased die Outcome 1. Frequency 205 154 141 165 145 190 Show that the likelihood of 0 based on these data is L(0) = C0395 (1 – 20)605, where C is a positive constant, not dependent on 0.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:Document1
Layout
References
Mailings
Review
O Tell me
View
Z Aa fx v sine X e* 0 - h - B9 -
gral Sum
Fonts
Formula Fraction Function Radical
Script Equation Statistical Matrix
Symbols
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
4
6.
Probability 0 (1 – 20) (1– 20) }(1- 20) (1- 20) 0
Table 2
Outcomes of 1000 independent rolls of a biased die
Outcome
1.
Frequency
205
154
141
165
145
190
Show that the likelihood of 6 based on these data is
L(0) = C0395 (1 – 20)605,
where C is a positive constant, not dependent on 0.
L'(0) = C0394(1 – 20)604 (395 – 2000 0).
1. What is the value of the maximum likelihood estimate, ô, of 0 based on these data?
Justify your answer.
2. What does the value of ê 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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