10. Let Y₁, Y₂,..., Yn be a random sample of size n from a gamma distribution with parameters and a both being 1. Is Y a pivotal quantity? Show why and why not is a pivotal quantity.
10. Let Y₁, Y₂,..., Yn be a random sample of size n from a gamma distribution with parameters and a both being 1. Is Y a pivotal quantity? Show why and why not is a pivotal quantity.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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Transcribed Image Text:10. Let Y₁, Y₂,..., Yn be a random sample of size n from a gamma distribution with
parameters and a both being 1. Is Y a pivotal quantity? Show why and why
not is a pivotal quantity.
11. Consider a random sample Y₁, Y₂, ..., Yn from a normal population Y~N(u,0²)
where the population variance and mean are unknown. We want to construct a
Σ(X₁-X)² Show
0²
100(1a)% confidence interval for the population variance if:
whether or not is a pivotal quantity and construct a 100(1-a) confidence
interval.
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