In a sequence of consecutive years 1, 2,...,T an annual number of bankruptcies are recorded by the central bank. The random counts N; , i = 1,2,...,T of bankruptcies in a given year are modeled using a Poisson(A) distribution and can be assumed independent from year to year. The central bank has collected data for the past six years and recorded the following counts: 2, 1, 1, 0, 2, 3. The prior on A is a Gamma(4, 4). Determine the posterior distribution h(A|N). Note: You may use that for a known a >0 and B > 0, the Gamma(a, B) density is given by: f(r; a, 3) = x> 0, %3D T(@)3a where Gamma(a) = e** da is the gamma function. Also, if X is distributed Gamma(a, B) then E(X) = aß and Var(X) = a8?. %3D Gamma ( 12, 10 Gamma 13 (뉴) Gamma Gamma ( 13, 10 1 Gamma( 10, 13

In a sequence of consecutive years 1, 2,...,T an annual number of bankruptcies are recorded by the central bank. The random counts N; , i = 1,2,...,T of bankruptcies in a given year are modeled using a Poisson(A) distribution and can be assumed independent from year to year. The central bank has collected data for the past six years and recorded the following counts: 2, 1, 1, 0, 2, 3. The prior on A is a Gamma(4, 4). Determine the posterior distribution h(A|N). Note: You may use that for a known a >0 and B > 0, the Gamma(a, B) density is given by: f(r; a, 3) = x> 0, %3D T(@)3a where Gamma(a) = e** da is the gamma function. Also, if X is distributed Gamma(a, B) then E(X) = aß and Var(X) = a8?. %3D Gamma ( 12, 10 Gamma 13 (뉴) Gamma Gamma ( 13, 10 1 Gamma( 10, 13

Name: b)The central bank (from part (a)) claims that the intensity is less
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Description: b)The central bank (from part (a)) claims that the intensity is less than 2. The central bank would liketo test the claim via Bayesian testing with a zero-one loss. Determine the value of the posteriorprobability required to perform this hypothesis

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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