Let X1,..., Xn be iid random variables from Poisson(A). Find a sufficient statistic for X. Use this sufficient statistic to find a better estimator of A than the e

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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Let X1,..., Xn be iid random variables from Poisson(A).
a)
Find a sufficient statistic for A.
b)
Use this sufficient statistic to find a better estimator of A than the estimator defined
by 01 = X1.
Let X1,..., Xn|A be iid Poisson(A), and let A
Give two reasons why this is a good choice of the prior distribution on ).
c)
Gamma(a, B), with a, B are known.
Transcribed Image Text:Let X1,..., Xn be iid random variables from Poisson(A). a) Find a sufficient statistic for A. b) Use this sufficient statistic to find a better estimator of A than the estimator defined by 01 = X1. Let X1,..., Xn|A be iid Poisson(A), and let A Give two reasons why this is a good choice of the prior distribution on ). c) Gamma(a, B), with a, B are known.
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ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,