b) From part (a) now suppose that we observe a sample of size ten with z; = 21. Let the prior be specified with parameters a = 1 and 3 = 4. Find an estimate for the parameter A using the squared error loss L(@, a) = (e- a). Give your answer to two decimal places. Hint: If X- Gamma(a, 3) then E(X) = a,3. Question Three Let X,...,X, be ii.d. Poisson(A) and let A have a Gamma(a, 3) distribution with density of the form, f(z,a, 3) - T(a)3" the conjugate family for the Poisson. Find the posterior distribution for A.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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b)
From part (a) now suppose that we observe a sample of size ten with zi = 21. Let the prior be specified
10
with parameters a = 1 and 3 = 4. Find an estimate for the parameter A using the squared error loss L(6, a) =
(0- a). Give your answer to two decimal places.
Hint: If X - Gamma(a, 3) then E(X) = a3.
Question Three
a)
Let X1,...., X be ii.d. Poisson(A) and let A have a Gamma(a, 8) distribution with density of the form,
f(z,a, 3) =
1
-le /
T(a)3"
the conjugate family for the Poisson. Find the posterior distribution for A.
Gamma
a+) X; + 1.
nB +1
Gamma
X.
n8 +1
a+
Gamma
a+>x
1
n3 +1
Gamma
a+
n8 +1)
(a+x:
Gamma
1
n3 +1
Transcribed Image Text:b) From part (a) now suppose that we observe a sample of size ten with zi = 21. Let the prior be specified 10 with parameters a = 1 and 3 = 4. Find an estimate for the parameter A using the squared error loss L(6, a) = (0- a). Give your answer to two decimal places. Hint: If X - Gamma(a, 3) then E(X) = a3. Question Three a) Let X1,...., X be ii.d. Poisson(A) and let A have a Gamma(a, 8) distribution with density of the form, f(z,a, 3) = 1 -le / T(a)3" the conjugate family for the Poisson. Find the posterior distribution for A. Gamma a+) X; + 1. nB +1 Gamma X. n8 +1 a+ Gamma a+>x 1 n3 +1 Gamma a+ n8 +1) (a+x: Gamma 1 n3 +1
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number marked thanks
Transcribed Image Text:Please complete and neat solved and option number marked thanks
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