Task 1. The points on opposite sides of a die add up to seven. Assume that you suspect that a die is biased towards rolling sixes. One possible model for the outcome X of a roll of this die would be to use the following probability mass function for X: 1 2 3 4 5 6 0 + { { { { { 0- { [x = 1 1 1 6. 6. 6 where 0 < 0 < is unknown. (a) Assume the die is rolled n = 100 times and we observe y = 32 sixes. (1) How would you model the outcome of this experiment? Clearly state your statistical model. (2) Using your model, find the likelihood function and the log-likelihood function of 0 (given the data). Using the log-likelihood function, also determine the score function. (3) Find the maximum likelihood estimate ô of 0 and its standard error.

Task 1. The points on opposite sides of a die add up to seven. Assume that you suspect that a die is biased towards rolling sixes. One possible model for the outcome X of a roll of this die would be to use the following probability mass function for X: 1 2 3 4 5 6 0 + { { { { { 0- { [x = 1 1 1 6. 6. 6 where 0 < 0 < is unknown. (a) Assume the die is rolled n = 100 times and we observe y = 32 sixes. (1) How would you model the outcome of this experiment? Clearly state your statistical model. (2) Using your model, find the likelihood function and the log-likelihood function of 0 (given the data). Using the log-likelihood function, also determine the score function. (3) Find the maximum likelihood estimate ô of 0 and its standard error.

Name: Task 1. The points on opposite sides of a die add up to seven. Assume
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Description: Task 1. The points on opposite sides of a die add up to seven. Assume that you suspect thata die is biased towards rolling sixes. One possible model for the outcome X of a roll of this diewould be to use the following probability mass function for X

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Profit and Loss

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Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.

Topic Video

Question

Task 1. The points on opposite sides of a die add up to seven. Assume that you suspect that
a die is biased towards rolling sixes. One possible model for the outcome X of a roll of this die
would be to use the following probability mass function for X:
1
2 3 4 5
Pr[X = x] - 0
1
6.
1
+ 0
|
6.
where 0 < 0 < is unknown.
(a) Assume the die is rolled n = 100 times and we observe y = 32 sixes.
(1) How would you model the outcome of this experiment? Clearly state your statistical
model.
(2) Using your model, find the likelihood function and the log-likelihood function of 0
(given the data). Using the log-likelihood function, also determine the score function.
(3) Find the maximum likelihood estimate ô of 0 and its standard error.
(4) Based on your model and the data, what conclusion do you draw about whether the
die is biased or not?
HINT: You may assume that the sampling distribution of your estimator is approx-
imately normal.

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