please answer part d,e,f,g only using r code showing the code and method Let x₁,..., n iid from N(u, o²) where o² is known.(a) Show that the Jeffreys prior for the normal likelihood isp(μ) = c₁ √n/o², μERfor some constant c₁ > 0.(b) Is this a proper prior or improrer prior? Explain.(c) Derive the posterior density for u under the normal likelihood N(μ, o²) and Jeffreysμprior for u. Plot the density.(d) Simulate 1,000 draws from the posterior derived in (c) and plot a histogram of thesimulated values.(e) Let 0 = exp(μ). Find the posterior density of analytically and plot the density.(f) Estimate by Monte Carlo integration.(g) Compute a 95% equal tail interval for analytically and by simulation.

Given that iid from where is known.

Let x₁,..., n iid from N(μ, o2) where o2 is known. (a) Show that the Jeffreys prior for the normal likelihood is p(μ) =₁₁√√√n/o², µER for some constant c₁ > 0. (b) Is this a proper prior or improrer prior? Explain. (c) Derive the posterior density for µ under the normal likelihood N(µ, o²) and Jeffreys prior for u. Plot the density. (d) Simulate 1,000 draws from the posterior derived in (c) and plot a histogram of the simulated values. (e) Let 0= exp(µ). Find the posterior density of analytically and plot the density. (f) Estimate by Monte Carlo integration. (g) Compute a 95% equal tail interval for analytically and by simulation.

Let x₁,..., n iid from N(μ, o2) where o2 is known. (a) Show that the Jeffreys prior for the normal likelihood is p(μ) =₁₁√√√n/o², µER for some constant c₁ > 0. (b) Is this a proper prior or improrer prior? Explain. (c) Derive the posterior density for µ under the normal likelihood N(µ, o²) and Jeffreys prior for u. Plot the density. (d) Simulate 1,000 draws from the posterior derived in (c) and plot a histogram of the simulated values. (e) Let 0= exp(µ). Find the posterior density of analytically and plot the density. (f) Estimate by Monte Carlo integration. (g) Compute a 95% equal tail interval for analytically and by simulation.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.CR: Chapter 13 Review

Problem 7CR

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