Suppose Y₁, Y2,, Yn is an iid sample from a gamma population distribution with shape parameter a = 2 and scale parameter 0, where > 0 is unknown. a. Find a function of the sample mean Y which is an unbiased estimator of 0. Also, find the variance of your unbiased estimator. b. Find two unbiased estimators of 7(0) = 0².

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.
Chapter1: Functions
Section1.2: The Least Square Line
Problem 1E
icon
Related questions
Question
Suppose Y₁, Y2,, Yn is an iid sample from a gamma population distribution with shape parameter
a = 2 and scale parameter 0, where > 0 is unknown.
a. Find a function of the sample mean Y which is an unbiased estimator of 0. Also, find the variance of
your unbiased estimator.
b. Find two unbiased estimators of 7(0) = 0².
Transcribed Image Text:Suppose Y₁, Y2,, Yn is an iid sample from a gamma population distribution with shape parameter a = 2 and scale parameter 0, where > 0 is unknown. a. Find a function of the sample mean Y which is an unbiased estimator of 0. Also, find the variance of your unbiased estimator. b. Find two unbiased estimators of 7(0) = 0².
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897…
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill