Suppose that X1,.., Xn is a random sample from the Poisson distribution with parameter 1 > 0. Let X and S? denote the sample mean and sample variance, respectively. (1) Show that (X,S²) is sufficient but not complete. (2) Prove the rather remarkable identity E(S2|X) = X.
Suppose that X1,.., Xn is a random sample from the Poisson distribution with parameter 1 > 0. Let X and S? denote the sample mean and sample variance, respectively. (1) Show that (X,S²) is sufficient but not complete. (2) Prove the rather remarkable identity E(S2|X) = X.
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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![Suppose that X1,..., X, is a random sample from the Poisson distribution with parameter
1 > 0. Let X and S denote the sample mean and sample variance, respectively.
(1) Show that (X, S²) is sufficient but not complete.
(2) Prove the rather remarkable identity E(S|X) = X.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa7ecb56a-ed81-4c0c-8e04-76ae7978c9ff%2F9776be54-1c8e-4917-b2bb-ae51f375ba2d%2F03kjyh_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose that X1,..., X, is a random sample from the Poisson distribution with parameter
1 > 0. Let X and S denote the sample mean and sample variance, respectively.
(1) Show that (X, S²) is sufficient but not complete.
(2) Prove the rather remarkable identity E(S|X) = X.
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