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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. The corresponding density is f(x) = Kra-le-Ba for a > 0 and f(x) = 0 elsewhere. You must use this parameterization for the problem. Suppose that a is known, but B is unknown. Find the posterior density of 3, f8|x (8 | æn), under prior B ~ Gam(a, b), where а. a > 0 and b > 0 are specified constants. b. Find the posterior mean of B.

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. The corresponding density is f(x) = Kra-le-Ba for a > 0 and f(x) = 0 elsewhere. You must use this parameterization for the problem. Suppose that a is known, but B is unknown. Find the posterior density of 3, f8|x (8 | æn), under prior B ~ Gam(a, b), where а. a > 0 and b > 0 are specified constants. b. Find the posterior mean of B.

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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Let X; > 0 be the total cost for subject i = 1, 2, ..., n. We model the data as X1, X2, . .., Xn id Gam(a, B). Here, Gam(a, B) indicates the Gamma distribution with shape a > 0 and rate B> 0. The corresponding density is f(x) : To Ta-le-B* for x > 0 and f(x) = 0 elsewhere. You must use this parameterization for the problem. Suppose that a is known, but B is unknown. Find the posterior density of B, fax (B | xn), under prior B ~ Gam(a, b), where а. a > 0 and b > 0 are specified constants. b. Find the posterior mean of ß.
Transcribed Image Text:Let X; > 0 be the total cost for subject i = 1, 2, ..., n. We model the data as X1, X2, . .., Xn id Gam(a, B). Here, Gam(a, B) indicates the Gamma distribution with shape a > 0 and rate B> 0. The corresponding density is f(x) : To Ta-le-B* for x > 0 and f(x) = 0 elsewhere. You must use this parameterization for the problem. Suppose that a is known, but B is unknown. Find the posterior density of B, fax (B | xn), under prior B ~ Gam(a, b), where а. a > 0 and b > 0 are specified constants. b. Find the posterior mean of ß.
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