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Consider independent observations (rı, y₁), ... (rn, yn), from the model Y₁ Bin(ri, p) for i = 1,...,n, where ther, are fixed constants. Using likelihood L(p) and log-likelihood (p) as appropriate, compute the following items. 1. Derive the maximum likelihood estimate p. 2. Write the second derivative of log-likelihood /(p). 3. Give an expression of the approximated asymptotic standard error of p by plugging in the estimate p. To )=√√√¹. this end, estimate the Fisher Information Matrix by Ý : == d ap² 1(p) and then s. e. (p) = p=p 4. Consider data (15,11), (20,14), (15,9), (10,7), (25,17), (15,12), (10,8). Using your formulæ, compute and write numerical estimates p, s. e. (p) and give a 95% confidence interval for p using the normal approximation.

Consider independent observations (rı, y₁), ... (rn, yn), from the model Y₁ Bin(ri, p) for i = 1,...,n, where ther, are fixed constants. Using likelihood L(p) and log-likelihood (p) as appropriate, compute the following items. 1. Derive the maximum likelihood estimate p. 2. Write the second derivative of log-likelihood /(p). 3. Give an expression of the approximated asymptotic standard error of p by plugging in the estimate p. To )=√√√¹. this end, estimate the Fisher Information Matrix by Ý : == d ap² 1(p) and then s. e. (p) = p=p 4. Consider data (15,11), (20,14), (15,9), (10,7), (25,17), (15,12), (10,8). Using your formulæ, compute and write numerical estimates p, s. e. (p) and give a 95% confidence interval for p using the normal approximation.

MATLAB: An Introduction with Applications
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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...., n, Consider independent observations (ri, y₁), ... (rn, yn), from the model Y₁ Bin(ri, p) for i = 1, ... where ther, are fixed constants. Using likelihood L(p) and log-likelihood /(p) as appropriate, compute the following items. 1. Derive the maximum likelihood estimate p. 2. Write the second derivative of log-likelihood /(p). 3. Give an expression of the approximated asymptotic standard error of p by plugging in the estimate p. To this end, estimate the Fisher Information Matrix by = -1(P) and then s. e. (p) = ») = √v p=p 4. Consider data (15,11), (20,14), (15,9), (10,7), (25,17), (15,12), (10,8). Using your formulæ, compute and write numerical estimates p, s. e. (p) and give a 95% confidence interval for p using the normal approximation.
Transcribed Image Text:...., n, Consider independent observations (ri, y₁), ... (rn, yn), from the model Y₁ Bin(ri, p) for i = 1, ... where ther, are fixed constants. Using likelihood L(p) and log-likelihood /(p) as appropriate, compute the following items. 1. Derive the maximum likelihood estimate p. 2. Write the second derivative of log-likelihood /(p). 3. Give an expression of the approximated asymptotic standard error of p by plugging in the estimate p. To this end, estimate the Fisher Information Matrix by = -1(P) and then s. e. (p) = ») = √v p=p 4. Consider data (15,11), (20,14), (15,9), (10,7), (25,17), (15,12), (10,8). Using your formulæ, compute and write numerical estimates p, s. e. (p) and give a 95% confidence interval for p using the normal approximation.
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