Applied Statistics and Probability for Engineers
6th Edition
ISBN: 9781118539712
Author: Douglas C. Montgomery
Publisher: WILEY
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Chapter 11, Problem 109SE
To determine
Explain whether the
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PEER REPLY 1:
Choose a classmate's Main Post and review their decision making process.
1. Choose a risk level for each of the states of nature (assign a probability
value to each).
2. Explain why each risk level is chosen.
3. Which alternative do you believe would be the best based on the maximum
EMV?
4. Do you feel determining the expected value with perfect information
(EVWPI) is worthwhile in this situation? Why or why not?
Questions
An insurance company's cumulative incurred claims for the last 5 accident years are given
in the following table:
Development Year
Accident Year 0
2018
1 2 3 4
245 267 274 289 292
2019
255 276 288 294
2020
265 283 292
2021
263 278
2022
271
It can be assumed that claims are fully run off after 4 years. The premiums received for
each year are:
Accident Year Premium
2018
306
2019
312
2020
318
2021
326
2022
330
You do not need to make any allowance for inflation.
1. (a) Calculate the reserve at the end of 2022 using the basic chain ladder method.
(b) Calculate the reserve at the end of 2022 using the Bornhuetter-Ferguson method.
2. Comment on the differences in the reserves produced by the methods in Part 1.
You are provided with data that includes all 50 states of the United States. Your task is to draw a sample of: o 20 States using Random Sampling (2 points: 1 for random number generation; 1 for random sample) o 10 States using Systematic Sampling (4 points: 1 for random numbers generation; 1 for random sample different from the previous answer; 1 for correct K value calculation table; 1 for correct sample drawn by using systematic sampling) (For systematic sampling, do not use the original data directly. Instead, first randomize the data, and then use the randomized dataset to draw your sample. Furthermore, do not use the random list previously generated, instead, generate a new random sample for this part. For more details, please see the snapshot provided at the end.) Upload a Microsoft Excel file with two separate sheets. One sheet provides random sampling while the other provides systematic sampling. Excel snapshots that can help you in organizing columns are provided on the next…
Chapter 11 Solutions
Applied Statistics and Probability for Engineers
Ch. 11.2 - 11-1. Diabetes and obesity are serious health...Ch. 11.2 - 11-2. On average, do people gain weight as they...Ch. 11.2 - Prob. 3ECh. 11.2 - 11-4. Regression methods were used to analyze the...Ch. 11.2 - 11-5. See Table E11-1 for data on the ratings of...Ch. 11.2 - 11-6. An article in Technometrics by S. C. Narula...Ch. 11.2 - 11-7. The number of pounds of steam used per month...Ch. 11.2 - 11-8. Go Tutorial Table E11-3 presents the highway...Ch. 11.2 - Prob. 9ECh. 11.2 - 11-10. An article in the Journal of Sound and...
Ch. 11.2 - Prob. 11ECh. 11.2 - 11-12. An article in the Journal of Environmental...Ch. 11.2 - 11-13. A rocket motor is manufactured by bonding...Ch. 11.2 - 11-14. Go Tutorial An article in the Journal of...Ch. 11.2 - 11-15 An article in the Journal of the...Ch. 11.2 - 11-16. An article in Wood Science and Technology...Ch. 11.2 - Prob. 17ECh. 11.2 - Prob. 18ECh. 11.2 - Prob. 19ECh. 11.2 - 11-20. Show that in a simple linear regression...Ch. 11.2 - 11-21. Consider the simple linear regression model...Ch. 11.2 - 11-22. Suppose that we wish to fit a regression...Ch. 11.4 - 11-23. Recall the regression of percent body fat...Ch. 11.4 - Prob. 24ECh. 11.4 - 11-25. Suppose that in Exercise 11-24 weight is...Ch. 11.4 - 11-26. Consider the simple linear regression model...Ch. 11.4 - Prob. 27ECh. 11.4 - Prob. 28ECh. 11.4 - Prob. 29ECh. 11.4 - Prob. 30ECh. 11.4 - 11-31. Consider the National Football League data...Ch. 11.4 - Prob. 32ECh. 11.4 - Prob. 33ECh. 11.4 - Prob. 34ECh. 11.4 - 11-35. Consider the data from Exercise 11-9 on y =...Ch. 11.4 - Prob. 36ECh. 11.4 - 11-37. Consider the data from Exercise 11-13, on y...Ch. 11.4 - 11-38. Consider the data from Exercise 11-12 on y...Ch. 11.4 - Prob. 39ECh. 11.4 - Prob. 40ECh. 11.4 - Prob. 41ECh. 11.4 - Prob. 42ECh. 11.4 - Prob. 44ECh. 11.6 - 11-45. Using the regression from Exercise...Ch. 11.6 - 11-46. Q Using the regression from Exercise...Ch. 11.6 - 11-47. Refer to the data in Exercise 11-3 on y =...Ch. 11.6 - 1-48. Exercise 11-4 presented data on roadway...Ch. 11.6 - 11-49. Refer to the NFL quarterback ratings data...Ch. 11.6 - Prob. 50ECh. 11.6 - 11-51. Exercise 11-7 presented data on y = steam...Ch. 11.6 - 11-52. Exercise 11-8 presented gasoline mileage...Ch. 11.6 - Prob. 53ECh. 11.6 - Prob. 54ECh. 11.6 - Prob. 55ECh. 11.6 - 11-56. Exercise 11-12 presented data on chloride...Ch. 11.6 - 11-57. Refer to the data in Exercise 11-13 on...Ch. 11.6 - Prob. 58ECh. 11.6 - Prob. 59ECh. 11.7 - 11-60. Consider the simple linear regression model...Ch. 11.7 - 11-61. Repeat Exercise 11-60 using an error term...Ch. 11.7 - 11-62. Refer to the compressive strength data in...Ch. 11.7 - 11-63. Refer to the NFL quarterback ratings data...Ch. 11.7 - 11-64. Refer to the data in Exercise 11-6 on...Ch. 11.7 - 11-65. Refer to the data in Exercise 11-7 on y =...Ch. 11.7 - 11-66. Refer to the gasoline mileage data in...Ch. 11.7 - Prob. 67ECh. 11.7 - Prob. 68ECh. 11.7 - 11-69. Refer to Exercise 11-12. which presented...Ch. 11.7 - Prob. 70ECh. 11.7 - 11-71. Consider the rocket propellant data in...Ch. 11.7 - 11-72. Consider the data in Exercise 11-9 on y =...Ch. 11.7 - Prob. 73ECh. 11.7 - Prob. 74ECh. 11.7 - Prob. 75ECh. 11.8 - 11-76. Suppose that data are obtained from 20...Ch. 11.8 - 11-77. Suppose that data are obtained from 20...Ch. 11.8 - Prob. 78ECh. 11.8 - 11-79. A random sample of 50 observations was made...Ch. 11.8 - 11-80. The data in Table E11-6 gave x = the water...Ch. 11.8 - Prob. 81ECh. 11.8 - 11-82. The weight and systolic blood pressure of...Ch. 11.8 - Prob. 83ECh. 11.8 - Prob. 84ECh. 11.8 - 11-85. Refer to the NFL quarterback ratings data...Ch. 11.8 - Prob. 86ECh. 11.9 - Prob. 87ECh. 11.9 - Prob. 88ECh. 11.9 - 11-89. An electric utility is interested in...Ch. 11.10 - Prob. 90ECh. 11.10 - 11-91. The compressive strength of an alloy...Ch. 11.10 - Prob. 92ECh. 11.10 - Prob. 93ECh. 11.10 - Prob. 94ECh. 11.10 - 11-95 Consider the propellant data is Exercise...Ch. 11 - Prob. 96SECh. 11 - Prob. 97SECh. 11 - 11-98. The strength of paper used in the...Ch. 11 - Prob. 99SECh. 11 - Prob. 100SECh. 11 - Prob. 101SECh. 11 - Prob. 102SECh. 11 - 11-103. An article in the Journal of Applied...Ch. 11 - 11-104. Two different methods can be used for...Ch. 11 - 11-105. The grams of solids removed from a...Ch. 11 - Prob. 106SECh. 11 - 11-107. The data in Table E11-20 related diamond...Ch. 11 - Prob. 108SECh. 11 - Prob. 109SECh. 11 - Prob. 110SECh. 11 - 11-111. Consider the simple linear regression...Ch. 11 - Prob. 112SECh. 11 - Prob. 113SECh. 11 - Prob. 114SECh. 11 - Prob. 115SECh. 11 - Prob. 116SE
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