Consider a random sample X1, X2, . . . , Xn from a distribution with pdf Let

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Consider a random sample X1, X2, . . . , Xn from a distribution with pdf
f(x|8) = 30x²e-r. 0 <x < oo.

Let θ have a prior pdf that is gamma with α = 4 and the usual θ = 1/4. Find the conditional mean of θ, given that X1 = x1, X2 = x2, . . . , Xn = xn.

Distribution
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Probability and Statistical Inference

ISBN: 978-0321923271

9th edition

Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

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