(b) Assume the die is rolled n = 100 times and we observe y = 32 sixes and z = 12 ones.(1) How would you model the outcome of this experiment? Clearly state your statisticalmodel.(2) Using your model, find the likelihood function and the log-likelihood function of 0(given the data).(3) Find the maximum likelihood estimate 0 of 0 and its standard error.(4) Based on your model and the data, what conclusion do you draw about whether thedie is biased or not?HINT: You may assume that the sampling distribution of your estimator is approx-imately normal. 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:12 3 4 56Pr[X = x] | – 011+ 06.6.where 0 < 0 < is unknown.

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(b) Assume the die is rolled n = 100 times and we observe y = 32 sixes and z = 12 ones. (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). (3) Find the maximum likelihood estimate 0 of 0 and its standard error.

(b) Assume the die is rolled n = 100 times and we observe y = 32 sixes and z = 12 ones. (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). (3) Find the maximum likelihood estimate 0 of 0 and its standard error.

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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Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

(b) Assume the die is rolled n = 100 times and we observe y = 32 sixes and z = 12 ones.
(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).
(3) Find the maximum likelihood estimate 0 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.

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
Pr[X = x] | – 0
1
1
+ 0
6.
6.
where 0 < 0 < is unknown.

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