### Questions1. **Distribution Suitability:** - 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. **Bias Estimation:** - Determine a way to estimate the bias of \( \hat{\theta} \) under the gamma model. Does it seem large in context?3. **Variance Estimation:** - Refer to the attached data table. The \( \hat{\sigma}_H \) column reports estimated standard deviations for each measurement. How might you use these to estimate \( \text{var}\hat{H} \)? Sketch out an approach by listing a few steps, and explain your reasoning.---### Supernova Data Table#### Supernova data from Freedman et al.| Supernova ID | Velocity (km/sec) | Distance (Mpc) | H (km/sec/Mpc) | \( \hat{\sigma}_H \) ||--------------|-------------------|----------------|----------------|-----------------|| SN1990O | 9065.00 | 134.70 | 67.30 | 2.30 || SN1990T | 12012.00 | 158.90 | 75.60 | 3.10 || SN1990af | 15055.00 | 198.60 | 75.80 | 2.80 || SN1991S | 16687.00 | 238.90 | 69.80 | 2.80 |*... [Data continues for all 36 supernovae] ...*---#### Table Explanation- **Columns:** - **Supernova ID:** Identification code for each supernova in the dataset. - **Velocity (km/sec):** Measured velocity of the supernova. - **Distance (Mpc):** Measured distance in megaparsecs. - **H (km/sec/Mpc):** Hubble constant derived for each supernova, indicating the rate of expansion of the universe relative to this specific observation. - **\( \hat{\sigma}_H \):** Estimated standard deviation of the Hubble constant measurement for each supernova.This data was used to measure the Hubble constant in a study

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.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks