1. Do you think the gamma distribution is a reasonable model for the data? What are the relevant considerations? Summarize your thoughts and conclusion(s) in 2-3 sentences. 2. Determine a way to estimate the bias of 0 under the gamma model. Does it seem large in context? 3. Refer to the attached data table. The ởH column reports estimated standard deviations for each measurement. How might you use these to estimate varH? Sketch out an approach by listing a few steps, and explain your reasoning. Supernova data from Freedman et al. Supernova ID SN1990O SN1990T Velocity (km/sec) Distance (Mpc) Н (km/sec/Mpс) 67.30 75.60 75.80 9065.00 134.70 2.30 12012.00 158.90 3.10 SN1990af 15055.00 198.60 2.80 SN1991S SN1991U SN1991ag SN1992J SN1992P 16687.00 238.90 69.80 2.80 83.70 73.70 74.50 64.80 9801.00 117.10 3.40 4124.00 56.00 2.90 13707.00 183.90 3.10 7880.00 121.50 2.20 SN1992ae 22426.00 274.60 81.60 3.40 SN1992ag SN1992al SN1992aq SN1992au SN1992bc 7765.00 102.10 76.10 2.70 72.80 64.70 4227.00 58.00 2.40 30253.00 467.00 2.40 18212.00 262.20 69.40 2.90 5935.00 88.60 67.00 2.10 SN1992bg SN1992bh SN1992bk SN1992B1 SN1992bo SN1992bp 70.60 66.70 73.60 72.70 10696.00 151.40 2.40 13518.00 202.50 2.30 17371.00 235.90 2.60 12871.00 176.80 2.60 5434.00 77.90 69.70 2.40 23646.00 309.50 391.50 280.10 303.40 236.10 215.40 119.70 202.30 76.30 2.60 SN1992br 26318.00 67.20 3.10 SN1992bs 18997.00 67.80 2.80 SN1993B SN19930 SN1993ag SN1993ah 21190.00 69.80 2.40 15567.00 65.90 2.10 15002.00 69.60 2.40 8604.00 71.90 2.90 72.90 75.60 74.90 68.00 72.50 71.50 SN1993A 14764.00 2.70 SN1993ae SN1994M 5424.00 71.80 3.10 7241.00 96.70 2.60 SN1994Q SN1994S SN1994T 8691.00 127.80 2.70 4847.00 66.80 2.50 10715.00 149.90 2.60 2.70 2.80 SN1995ac 14634.00 185.60 78.80 SN1995ak 6673.00 82.40 80.90 SN1996C SN199661 9024.00 136.00 66.30 2.50 10446.00 132.70 78.70 2.70 Table 1: Velocity and distance measurements for 36 type la supernovae. Data from Freedman, Wendy L., et al. "Final results from the Hubble Space Telescope key project to measure the Hubble constant." The Astrophysical Journal 553.1 (2001): 47.
1. Do you think the gamma distribution is a reasonable model for the data? What are the relevant considerations? Summarize your thoughts and conclusion(s) in 2-3 sentences. 2. Determine a way to estimate the bias of 0 under the gamma model. Does it seem large in context? 3. Refer to the attached data table. The ởH column reports estimated standard deviations for each measurement. How might you use these to estimate varH? Sketch out an approach by listing a few steps, and explain your reasoning. Supernova data from Freedman et al. Supernova ID SN1990O SN1990T Velocity (km/sec) Distance (Mpc) Н (km/sec/Mpс) 67.30 75.60 75.80 9065.00 134.70 2.30 12012.00 158.90 3.10 SN1990af 15055.00 198.60 2.80 SN1991S SN1991U SN1991ag SN1992J SN1992P 16687.00 238.90 69.80 2.80 83.70 73.70 74.50 64.80 9801.00 117.10 3.40 4124.00 56.00 2.90 13707.00 183.90 3.10 7880.00 121.50 2.20 SN1992ae 22426.00 274.60 81.60 3.40 SN1992ag SN1992al SN1992aq SN1992au SN1992bc 7765.00 102.10 76.10 2.70 72.80 64.70 4227.00 58.00 2.40 30253.00 467.00 2.40 18212.00 262.20 69.40 2.90 5935.00 88.60 67.00 2.10 SN1992bg SN1992bh SN1992bk SN1992B1 SN1992bo SN1992bp 70.60 66.70 73.60 72.70 10696.00 151.40 2.40 13518.00 202.50 2.30 17371.00 235.90 2.60 12871.00 176.80 2.60 5434.00 77.90 69.70 2.40 23646.00 309.50 391.50 280.10 303.40 236.10 215.40 119.70 202.30 76.30 2.60 SN1992br 26318.00 67.20 3.10 SN1992bs 18997.00 67.80 2.80 SN1993B SN19930 SN1993ag SN1993ah 21190.00 69.80 2.40 15567.00 65.90 2.10 15002.00 69.60 2.40 8604.00 71.90 2.90 72.90 75.60 74.90 68.00 72.50 71.50 SN1993A 14764.00 2.70 SN1993ae SN1994M 5424.00 71.80 3.10 7241.00 96.70 2.60 SN1994Q SN1994S SN1994T 8691.00 127.80 2.70 4847.00 66.80 2.50 10715.00 149.90 2.60 2.70 2.80 SN1995ac 14634.00 185.60 78.80 SN1995ak 6673.00 82.40 80.90 SN1996C SN199661 9024.00 136.00 66.30 2.50 10446.00 132.70 78.70 2.70 Table 1: Velocity and distance measurements for 36 type la supernovae. Data from Freedman, Wendy L., et al. "Final results from the Hubble Space Telescope key project to measure the Hubble constant." The Astrophysical Journal 553.1 (2001): 47.
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Transcribed Image Text:1. Do you think the gamma distribution is a reasonable model for the data? What are the
relevant considerations? Summarize your thoughts and conclusion(s) in 2-3 sentences.
2. Determine a way to estimate the bias of 0 under the gamma model. Does it seem large in
context?
3. Refer to the attached data table. The ôH column reports estimated standard deviations for
each measurement. How might you use these to estimate varH? Sketch out an approach by
listing a few steps, and explain your reasoning.
Supernova data from Freedman et al.
Supernova ID
SN19900
Velocity (km/sec)
Н (km/sec/Mрс)
Distance (Mpc)
9065.00
134.70
67.30
2.30
SN1990T
SN1990af
12012.00
158.90
75.60
3.10
15055.00
198.60
75.80
2.80
16687.00
69.80
83.70
SN1991S
238.90
2.80
SN1991U
9801.00
117.10
3.40
SN1991ag
SN1992J
4124.00
56.00
73.70
2.90
13707.00
183.90
74.50
3.10
SN1992P
7880.00
121.50
64.80
2.20
SN1992ae
22426.00
274.60
81.60
3.40
SN1992ag
SN1992al
SN1992aq
SN1992au
SN1992bc
7765.00
102.10
76.10
2.70
4227.00
58.00
72.80
2.40
30253.00
467.00
64.70
2.40
18212.00
262.20
69.40
2.90
5935.00
88.60
67.00
2.10
SN1992bg
SN1992bh
10696.00
151.40
70.60
2.40
13518.00
202.50
66.70
2.30
SN1992BK
17371.00
235.90
73.60
2.60
SN1992B1
12871.00
176.80
72.70
2.60
SN1992B0
5434.00
77.90
69.70
2.40
SN1992bp
23646.00
309.50
76.30
2.60
SN1992br
26318.00
391.50
67.20
3.10
SN1992BS
18997.00
280.10
67.80
2.80
SN1993B
21190.00
303.40
69.80
2.40
SN19930
SN1993ag
SN1993ah
15567.00
236.10
65.90
2.10
15002.00
215.40
69.60
2.40
8604.00
119.70
71.90
2.90
SN1993ac
14764.00
202.30
72.90
2.70
SN1993ae
5424.00
71.80
75.60
3.10
SN1994M
7241.00
96.70
74.90
2.60
SN1994Q
SN1994S
SN1994T
8691.00
127.80
68.00
2.70
4847.00
66.80
72.50
2.50
10715.00
149.90
71.50
2.60
SN1995ac
14634.00
185.60
78.80
2.70
SN1995ak
SN1996C
6673.00
82.40
80.90
2.80
9024.00
136.00
66.30
2.50
SN199661
10446.00
132.70
78.70
2.70
Table 1: Velocity and distance measurements for 36 type la supernovae. Data from Freedman,
Wendy L., et al. "Final results from the Hubble Space Telescope key project to measure the
Hubble constant." The Astrophysical Journal 553.1 (2001): 47.
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