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b) Suppose that X₁, X2, ..., Xn denotes a random samples from a gamma distribution f(x; a, B). i) What will be the minimal sufficient statistic for ß? Explain. 2 ΣΕ, Χι is a pivotal quantity. B ii) If a = 2, use the appropriate method to show that Y = iii) Given that a random sample of heavy machines from Polokwane factory produced the following noise levels 85.4, 86.8, 86.1, 85.3 and 84.8. Use part ii) of question 3 b) to construct a 95% confidence interval for B.

b) Suppose that X₁, X2, ..., Xn denotes a random samples from a gamma distribution f(x; a, B). i) What will be the minimal sufficient statistic for ß? Explain. 2 ΣΕ, Χι is a pivotal quantity. B ii) If a = 2, use the appropriate method to show that Y = iii) Given that a random sample of heavy machines from Polokwane factory produced the following noise levels 85.4, 86.8, 86.1, 85.3 and 84.8. Use part ii) of question 3 b) to construct a 95% confidence interval for B.

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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b) Suppose that X₁, X2, ..., Xn denotes a random samples from a gamma distribution f(x; a, ß). i) What will be the minimal sufficient statistic for ß? Explain. ii) If a = 2, use the appropriate method to show that Y = 2₁1 Xi B is a pivotal quantity. iii) Given that a random sample of heavy machines from Polokwane factory produced the following noise levels 85.4, 86.8, 86.1, 85.3 and 84.8. Use part ii) of question 3 b) to construct a 95% confidence interval for B.
Transcribed Image Text:b) Suppose that X₁, X2, ..., Xn denotes a random samples from a gamma distribution f(x; a, ß). i) What will be the minimal sufficient statistic for ß? Explain. ii) If a = 2, use the appropriate method to show that Y = 2₁1 Xi B is a pivotal quantity. iii) Given that a random sample of heavy machines from Polokwane factory produced the following noise levels 85.4, 86.8, 86.1, 85.3 and 84.8. Use part ii) of question 3 b) to construct a 95% confidence interval for B.
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