Let H denote the true Hubble constant. The age of the universe can be expressed in years as where e is the conversion factor Mpe/km) Cwear) = 978, 440, 076,094. 1. Consider 6 - cH-, Compute an estimate of 6 using the estimator 0 and the supernova data. %3D id 2. Now suppose that H,. H36 gamma(a, 3) with density f(h)- F(a) h>0 !! (a) What is the distribution of H? (b) Show that U = H- has an inverse gamma distribution with density (n8) na) T(na) g(u) = no-1,- (Hint: for z> 0, the function is monotone decreasing.)

Linear Algebra: A Modern Introduction
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ISBN:9781285463247
Author:David Poole
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Chapter6: Vector Spaces
Section6.7: Applications
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i need Q2 part B

Part 1: individual
Let H denote the true Hubble constant. The age of the universe can be expressed in years as
H.
where e is the conversion factor Mpe/km)
Cyrar)
= 978, 440, 076,094.
1. Consider 0 = cH-, Compute an estimate of 6 using the estimator 8 and the supernova data.
%3D
2. Now suppose that H1,..., H36 gamma(a, 3) with density
f(h) =
h>0
F(a)
(a) What is the distribution of H?
(b) Show that U = H-' has an inverse gamma distribution with density
(n8) na)
g(u) =
T(na)
%3D
(Hint: for z> 0, the function is monotone decreasing.)
Transcribed Image Text:Part 1: individual Let H denote the true Hubble constant. The age of the universe can be expressed in years as H. where e is the conversion factor Mpe/km) Cyrar) = 978, 440, 076,094. 1. Consider 0 = cH-, Compute an estimate of 6 using the estimator 8 and the supernova data. %3D 2. Now suppose that H1,..., H36 gamma(a, 3) with density f(h) = h>0 F(a) (a) What is the distribution of H? (b) Show that U = H-' has an inverse gamma distribution with density (n8) na) g(u) = T(na) %3D (Hint: for z> 0, the function is monotone decreasing.)
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