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Let X; > 0 be the total cost for subject i = 1,2, ... , n. We model the data as X1, X2, ..., Xn Gam(a, B). Here, Gam(a, B) indicates the Gamma distribution with shape a > 0 and rate B>0. The corresponding density is f(æ) = oa-le-Bæ for r > 0 and f(x) = 0 elsewhere. You must %3D use this parameterization for the problem. Suppose that a is known, but 3 is unknown. Find the posterior density of B, f3jx (B | æn), under prior 3 ~ Gam(a, b), where а. a >0 and b > 0 are specified constants. b. Find the posterior mean of ß.

Let X; > 0 be the total cost for subject i = 1,2, ... , n. We model the data as X1, X2, ..., Xn Gam(a, B). Here, Gam(a, B) indicates the Gamma distribution with shape a > 0 and rate B>0. The corresponding density is f(æ) = oa-le-Bæ for r > 0 and f(x) = 0 elsewhere. You must %3D use this parameterization for the problem. Suppose that a is known, but 3 is unknown. Find the posterior density of B, f3jx (B | æn), under prior 3 ~ Gam(a, b), where а. a >0 and b > 0 are specified constants. b. Find the posterior mean of ß.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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iid Let X; > 0 be the total cost for subject i = 1, 2, ..., n. We model the data as X1, X2, ... , Xn Gam(a, B). Here, Gam(a, B) indicates the Gamma distribution with shape a > 0 and rate B > 0. Ba The corresponding density is f(x) = Hora-le-Ba for x > 0 and f(x) = 0 elsewhere. You must %3D use this parameterization for the problem. Suppose that a is known, but 3 is unknown. Find the posterior density of B, fg|x (B | xn), under prior 3 ~ Gam(a, b), where а. a > 0 and b > 0 are specified constants. b. Find the posterior mean of ß.
Transcribed Image Text:iid Let X; > 0 be the total cost for subject i = 1, 2, ..., n. We model the data as X1, X2, ... , Xn Gam(a, B). Here, Gam(a, B) indicates the Gamma distribution with shape a > 0 and rate B > 0. Ba The corresponding density is f(x) = Hora-le-Ba for x > 0 and f(x) = 0 elsewhere. You must %3D use this parameterization for the problem. Suppose that a is known, but 3 is unknown. Find the posterior density of B, fg|x (B | xn), under prior 3 ~ Gam(a, b), where а. a > 0 and b > 0 are specified constants. b. Find the posterior mean of ß.
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