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.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
Problem 2AGP
Related questions
Question
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc7f442cf-541d-4442-b6c8-0606c8499d0b%2Fc443dc51-f547-4836-a5cc-5942ddb9b6f9%2Ftum6ecf_processed.jpeg&w=3840&q=75)
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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