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Now suppose we have only one sample x₁,...,n from the density: ƒ(x|t) = (2π)−¹/27¹/2−0.5x², x € (-∞, +∞), here T> 0 is an unknown parameter. (*)

Now suppose we have only one sample x₁,...,n from the density: ƒ(x|t) = (2π)−¹/27¹/2−0.5x², x € (-∞, +∞), here T> 0 is an unknown parameter. (*)

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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2. Now suppose we have only one sample x₁, ..., xn from the density: ƒ(x|t) = (2π)−¹/2+¹/2 −0.5x², x € (-∞, +∞), where T> 0 is an unknown parameter. Consider the following prior for T: ~ I'(a, b). T~ Note. The density of I' (a, b) distribution is f(x) e - fa r(a) ra-1 (*) -bx e , x > 0, with mean a/b and variance a/b².
Transcribed Image Text:2. Now suppose we have only one sample x₁, ..., xn from the density: ƒ(x|t) = (2π)−¹/2+¹/2 −0.5x², x € (-∞, +∞), where T> 0 is an unknown parameter. Consider the following prior for T: ~ I'(a, b). T~ Note. The density of I' (a, b) distribution is f(x) e - fa r(a) ra-1 (*) -bx e , x > 0, with mean a/b and variance a/b².
a) Derive the density of the posterior distribution of given ï₁, . . . , ¤n, and show that it is I'(A, B), with A and B depending only on a, b, n and x₁, ..., n. For observed data with n= 43 and Σ; x² = 56.3, and prior with a = 0.25, b = 0.5, determine the values of A and B (give exactly 2 d.p.): A = B =
Transcribed Image Text:a) Derive the density of the posterior distribution of given ï₁, . . . , ¤n, and show that it is I'(A, B), with A and B depending only on a, b, n and x₁, ..., n. For observed data with n= 43 and Σ; x² = 56.3, and prior with a = 0.25, b = 0.5, determine the values of A and B (give exactly 2 d.p.): A = B =
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