Given that E{X) = X and var {X) = X for the Poisson distribution, show that sample

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Given that E{X) = X and var {X) = X for the Poisson distribution, show that sample means based on samples of N independent observations from a Poisson process are

(a) unbiased estimators of X

(b) distributed with variance \/N

(c) consistent estimators of X

(d) relatively more efficient as estimators of X than are means based on samples of size N — 1.

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Statistics Probability Inference And Decision

ISBN: 9780030778056

1st Edition

Authors: Robert L. Winkler, William L. Hays

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Question Posted: Sep 21, 2024 09:02 AM

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Given that E{X) = X and var {X) = X for the Poisson distribution, show that sample

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Statistics Probability Inference And Decision

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