Consider X1, · · · , Xn|μ i.i.d ∼ N (μ, σ2), where σ2 is known. The prior distribution of μ is N (μ0, σ2 0 ), where μ0 and σ2 0 are known. (a) Show that ˆμBayes is just the prior mean with no data given but is the sample mean in large samples. (b) Your prior distribution for μ is N (10, 25). Compute the prior probability that μ is larger than 20. Hint: Use the normal table or R function pnorm. (c) Suppose you know V ar(Xi) = 5 and your sample of size 50 has the average value of 20. With the prior distribution in (b), compute the posterior probability that μ is larger than 20. Hint: Use the normal table or R function pnorm.
Consider X1, · · · , Xn|μ i.i.d ∼ N (μ, σ2), where σ2 is known. The prior distribution of μ is N (μ0, σ2 0 ), where μ0 and σ2 0 are known. (a) Show that ˆμBayes is just the prior mean with no data given but is the sample mean in large samples. (b) Your prior distribution for μ is N (10, 25). Compute the prior probability that μ is larger than 20. Hint: Use the normal table or R function pnorm. (c) Suppose you know V ar(Xi) = 5 and your sample of size 50 has the average value of 20. With the prior distribution in (b), compute the posterior probability that μ is larger than 20. Hint: Use the normal table or R function pnorm.
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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Question
Consider X1, · · · , Xn|μ i.i.d
∼ N (μ, σ2), where σ2 is known. The prior distribution of μ is N (μ0, σ2
0 ), where μ0
and σ2
0 are known.
(a) Show that ˆμBayes is just the prior
(b) Your prior distribution for μ is N (10, 25). Compute the prior
Hint: Use the normal table or R
(c) Suppose you know V ar(Xi) = 5 and your sample of size 50 has the average value of 20. With the prior
distribution in (b), compute the posterior probability that μ is larger than 20.
Hint: Use the normal table or R function pnorm.
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