Let y 1 , y 2 , y 3 , . . . , y n ,

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Let y1, y2, y3, . . . , yn, represent a random sample of size n selected from a Poisson probability distribution with unknown mean λ. Let X represent the sum of the Poisson values, X = ∑Yi    . Then X has a Poisson distribution with mean nλ. Assume that the prior distribution for λ is an exponential probability distribution with parameter β.
a. Find the posterior distribution, g(λ Ι x).
b. Using a squared error loss function, find the Bayesian estimate of λ.

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Statistics For Engineering And The Sciences

ISBN: 9781498728850

6th Edition

Authors: William M. Mendenhall, Terry L. Sincich

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