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(1) The mean and variance of y, are, respectively,

(1) The mean and variance of y, are, respectively,

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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Problem 1 Consider the mixed effects model Y₁ = a + b₁x + σei, with b;= N(μ, 7²). (1) The mean and variance of yi are, respectively, Problem 2 With the same model as in Problem 1, prior distributions are assigned to λ = 1/0², now assumed unknown, and μ, with a and 72 known. The prior for A is gamma(1, 1) and the prior for μ is N (0, 10²). Using a Gibbs sampler algorithm. (5) If a = 0 and o is known, the posterior distribution for μ is normal with mean and variance (let o² = x² 7² +0²) O O () 12²/²+1/10 1²/0²+1/10) Σ₁-13,21/0² -1 2²/0²+1/100 E 2²/0²+1/100 ΣπίσηΣ /6+1/100, ਵ
Transcribed Image Text:Problem 1 Consider the mixed effects model Y₁ = a + b₁x + σei, with b;= N(μ, 7²). (1) The mean and variance of yi are, respectively, Problem 2 With the same model as in Problem 1, prior distributions are assigned to λ = 1/0², now assumed unknown, and μ, with a and 72 known. The prior for A is gamma(1, 1) and the prior for μ is N (0, 10²). Using a Gibbs sampler algorithm. (5) If a = 0 and o is known, the posterior distribution for μ is normal with mean and variance (let o² = x² 7² +0²) O O () 12²/²+1/10 1²/0²+1/10) Σ₁-13,21/0² -1 2²/0²+1/100 E 2²/0²+1/100 ΣπίσηΣ /6+1/100, ਵ
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