)Is 6 consistent for 0?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
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i need Q2 part D

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.)
(c) Assume that H==EH,. Express 0 in terms of a and B. What is bias(0)?
%3D
(Note: you do not need to calculate the mean of Jan inverse gamma random variable
look up the mean in a distribution table or on Wikipedia.)
(d) Is é consistent for 0?
Transcribed Image Text:(c) Assume that H==EH,. Express 0 in terms of a and B. What is bias(0)? %3D (Note: you do not need to calculate the mean of Jan inverse gamma random variable look up the mean in a distribution table or on Wikipedia.) (d) Is é consistent for 0?
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