Question

In: Math

Terry is a small business entrepreneur and owns 6 buildings for business use. The probability distribution...

Terry is a small business entrepreneur and owns 6 buildings for business use. The probability distribution below describes expected property losses for the group of 6 buildings. Assume that the property exposures are independent of each other.

Losses $                                                          Probability of Loss

$10,000                                                           0.20

$20,000                                                           0.10

$50,000                                                           0.06

$100,000                                                         0.03

$500,000                                                         0.01

Now suppose Terry joins a risk sharing arrangement with other small business owners and now a total of 18 buildings are in the risk sharing pool. Assume that the property losses for the additional buildings follow the same probability distribution as that given for Terry’s buildings and losses are independent.

a. Find the average or expected loss of this larger group of buildings in a given year.

b. Calculate the standard deviation of the distribution.

c. Find the Coefficient of Variation

d. What happens to variance or risk for Terry after the sharing arrangement is in place?

e. What would you expect to happen to variance or risk if the pool was extremely large? Why?

f. What is Terry’s actuarially fair premium now? What has happened to his risk premium now?

Solutions

Expert Solution

a. Find the average or expected loss of this larger group of buildings in a given year.

b. Calculate the standard deviation of the distribution.

We have found the mean = 15000 and sd = 52773.0992 for a group of 6 buildings.

We need to find the mean and sd for the large group which is equal

mean = 15000* 3 = 45000

sd = 52773.0992*3 = 158319.5


c.

d. The variance increases by 3 times


Related Solutions

Terry is a small business entrepreneur and owns 6 buildings for business use. The probability distribution...
Terry is a small business entrepreneur and owns 6 buildings for business use. The probability distribution below describes expected property losses for the group of 6 buildings. Assume that the property exposures are independent of each other. Losses $                                                          Probability of Loss $10,000                                                           0.20 $20,000                                                           0.10 $50,000                                                           0.06 $100,000                                                         0.03 $500,000                                                         0.01 Find the average or expected loss of the group of buildings in a given year. Calculate the standard deviation of the distribution. Find the Coefficient of Variation....
What is a probability distribution? What is a continuous probability distribution? Provide an example from business...
What is a probability distribution? What is a continuous probability distribution? Provide an example from business of the usefulness of a probability distribution and/or a continuous probability.
Use the probability distribution to find probabilities in parts​ (a) through​ (c). The probability distribution of...
Use the probability distribution to find probabilities in parts​ (a) through​ (c). The probability distribution of number of dogs per household in a small town Dogs 0 1 2 3 4 5 Households 0.6730.673 0.2010.201 0.0760.076 0.0250.025 0.0170.017 0.0080.008 ​(a) Find the probability of randomly selecting a household that has fewer than two dogs. 0.8740.874   ​(Round to three decimal places as​ needed.) ​(b) Find the probability of randomly selecting a household that has at least one dog. 0.3270.327 ​ (Round...
Project yourself as an entrepreneur of a small scale business in your country: Business Plan format...
Project yourself as an entrepreneur of a small scale business in your country: Business Plan format required. A title page, (a) General Business Description • Mission Statements • Company goals and objectives (b) Business Philosophy • Target Customer • Industry Description: Is it a growth industry? What long term or Short term changes do you foresee in the industry? How will your company take advantage of it? • Company strengths and core competencies: What factors will make the company succeed?...
Assume yourself as an entrepreneur of a small scale business ( Restaurant ) Financial Plan The...
Assume yourself as an entrepreneur of a small scale business ( Restaurant ) Financial Plan The financial plan consists of a 12‐month profit and loss projection, a cash‐flow projection, a projected balance sheet, and a break‐even calculation. Together they constitute a reasonable estimate of your company’s financial future.
How can a business manager use Binomial probability distribution to assess a profitability of a new...
How can a business manager use Binomial probability distribution to assess a profitability of a new firm?
a/Use Excel to find the discrete probability and cumulative probability of the Binomial distribution with probability...
a/Use Excel to find the discrete probability and cumulative probability of the Binomial distribution with probability of success p = 0.75 and n = 80. Find its mean and variance. b/Based upon Excel chart, what can you conclude about the binomial convergence? Hint: Use binom.dist function on Excel and sketch the curve.
In downtown Metropolis, Mr. Kent owns several small office buildings in which he rents space to...
In downtown Metropolis, Mr. Kent owns several small office buildings in which he rents space to various professionals. Last year he sold two of his rental buildings. Mr. Kent sold one of the buildings, Lois Lane Office Suites, for $450,000; Mr. Kent’s basis in Lois Lane Office Suites was $400,000. Mr. Kent sold the second building, Kryptonite Professional Center, for $470,000. Mr. Kent’s basis in Kryptonite Professional Center was $540,000. He had owned both buildings for several years. Depreciation claimed...
1- What is the difference between: a. Entrepreneurship. b. Small business management. c. Entrepreneur. d. small...
1- What is the difference between: a. Entrepreneurship. b. Small business management. c. Entrepreneur. d. small business manager.
Assume yourself as an entrepreneur of a small scale business in Saudi Arabia. I chose a...
Assume yourself as an entrepreneur of a small scale business in Saudi Arabia. I chose a coffee shop project Assignment Objectives & Requirements: • Describe your Industry: Is it a growth industry? What long term or Short term changes do you foresee in the industry? How will your company take advantage of it? • Describe your most important company strengths and core competencies: What factors will make the company succeed? What do you think your major competitive strengths will be?...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT