Gene A has two alleles, A1 and A2. Gene B has two alleles, B1 and B2. In a population, the following haplotypes are observed. A1B1 = 0.2, A2B2 = 0.45, A1B2 = 0.15, and A2B1 = 0.2. Calculate the extent of linkage disequilibrium, D.

4. you are trying to develop a strategy for investing in two different stocks. The anticipated annual return for a $1,000 investment in each stock under four different economic conditions has the following probability distribution:

a. Expected return for stock X and for stock Y.

b. Standard deviation for stock X and for stock Y.

c. Covariance of stock X and stock Y.

d. Would you invest in stock X or stock Y? Explain

Suppose the installation time in hours for a software on a laptop has probability density function f(x) = (4/3) (1 − x³ ), 0 ≤ x ≤ 1.

(a) Find the probability that the software takes between 0.3 and 0.5 hours to be installed on your laptop.

(b) Let X₁, . . . , X₃₀ be the installation times of the software on 30 different laptops. Assume the installation times are independent. Find the probability that the average installation time is between 0.3 and 0.5 hours. Cite the theorem you use.

(c) Instead of taking a sample of 30 laptops as in the previous question, you take a sample of 60 laptops. Find the probability that the average installation time is between 0.3 and 0.5 hours. Cite the theorem you use.

Review Question

1. What is sales revenue forecasting?

2. What types of data are needed to forecast sales or revenues?

3. What is cost estimation?

4. What is the first step managers need to complete when estimating costs?

20. How does technology affect costs?

22. Identify three environmental factors that affect business decisions related to costs.

25. How does technological innovation generally affect a firm' s costs?

27. What is meant by the learning curve?

28. What are controllable costs?

Exercise and Problems

6. Mega Profits Company estimated its annual total cost function to be: Y = $150,000 + $.57 x Assuming that Y represents total cost and x equals the number of units sold, use this equation to answer the following questions:

a. What is the firm' s total fixed cost?

b. What is the firm' s variable cost per unit?

c. Compute total costs if the firm sells 100,000 units.

d. Compute total costs if the firm sells 200,000 units.

e.  If the firm' s product sells for $1.00, how many units does the firm need to sell to break even?

f.  If the firm' s product sells for $1.50, how many units does the firm need to sell to break even?

7. Morrison Hotel uses its banquet room to host parties, dinner dances, and business meetings. The hotel serves meals and provides a variety of services for each event. A local consultant analyzed recent cost data and estimated the total cost function per event to be as follows: Y = $1,000 + $9.00 x Assuming that Y represents total cost and x equals the number of guests, use this equation to answer the following questions:

a. What is the firm' s total fixed cost per event?

b. What is the firm' s variable cost per guest?

c. Compute total costs if 50 guests attend the event.

d.  Compute total costs if 100 guests attend an event.

e.  If the hotel charges $25.00 per guest, how many guests must attend for the hotel to break even at each event?

f.  If the hotel charges $28.00 per guest, how many guests must attend for the hotel to break even at each event?

g.  If the hotel charges $28.00 per guest, would you advise this hotel to host events for 50 or fewer guests? Why or why not?

3. Durango Mountain Bike Company wants to open a bicycle repair shop in a suburb of a major metropolitan area. The industry association estimates that 20 percent of bicycles are repaired by similar service companies and that the average owner spends $100 per bicycle on maintenance each year. The census and local chamber of commerce data indicate that there are 10,000 bicycles in the county. Three other competitors exist within a twenty-five-mile radius of the proposed business location. Based on a consumer survey, the owners believe that they can capture 30 percent of the market in the first year of operation. Based on these data, address the following requirements:

a.  What is the potential number of bicycles likely to be commercially repaired?

b. What is the total potential bicycle repair revenue available in the market?

c. How much revenue can Durango Mountain Bike expect to generate?

You are given the sample mean and the population standard deviation. Use this information to construct the​ 90% and​ 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. If​ convenient, use technology to construct the confidence intervals.

A random sample of 35 home theater systems has a mean price of ​$144.00. Assume the population standard deviation is $15.90.

A. Construct a 90% confidence interval for the population mean.

The 90% confidence interval is (__,__)

You are given the sample mean and the population standard deviation. Use this information to construct the​ 90% and​ 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. If​convenient, use technology to construct the confidence intervals.

A random sample of 50 home theater systems has a mean price of ​$130.00. Assume the population standard deviation is $15.50.

Construct a​ 90% confidence interval for the population mean.

The​ 90% confidence interval is __,__

You are given the sample mean and the population standard deviation. Use this information to construct the​ 90% and​ 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. If​ convenient, use technology to construct the confidence intervals.

A random sample of 60 home theater systems has a mean price of $111.00. Assume the population standard deviation is $16.20.

The 90% confidence interval is(--,--)

The 99% confidence interval is(--,--)

Which interval is wider?

In Python

Suppose there is a movie theater who charges ticket based on ages. Less than 3 years old, free; between 3 to 12, $10; more than 12 years old, $15. Please design a program with loop to,

1) Ask the name then age of the audience,

2) Based on audience's input, tell the audience (with the person's name) how much is the ticket,

3) Stop the program when type in 'quit' in your program.

Which of the following is an example of adverse possession?

B. Sally owned a one-acre lot next to a state park. She decided to donate the lot to the state in order to expand the park. Sally’s children claimed they had a right to the land, not the state.

C. In 2005, Megan fenced off a field belonging to Farmer Giles, put a new lock on the gate leading to the field, built a wooden shed, and grew vegetables on the land. After 10 years, Megan gained title to the land without paying Farmer Giles.

D. Bob needed a place to stay so he broke into an empty house and stayed there for nearly a month until the house owner asked the police to make Bob leave.

A. Years ago, your grandmother bought 10 acres of land, paid the property taxes, and left you the property in her will.

A landowner builds a nine-foot fence topped with barbed wire around his property to keep people out, and posts warning signs on the fence saying “DANGER: Barbed Wire.” A group of graduate students decides to go cow tipping on the landowner’s property. The students climb the fence in the night, and one student suffers injuries from the barbed wire. What duty of care does the landowner owe to the students?

D. No duty because the student trespassed onto the owner’s land

B. A duty not to intentionally injure and to warn about known defects on the property

A. A duty not to intentionally injure the student

C. A duty to inspect the property for defects, correct defects, and warn about defects

Marta places a large, pre-assembled plastic greenhouse in her backyard, with the steel frame bolted into concrete that she poured specially for that purpose. She attaches gas-heating ducts and builds a brick walkway around the greenhouse. Now the town wants to raise her real property taxes, claiming that her property has been improved. Marta argues that the greenhouse is not real property. Is it?

E. The greenhouse is an easement and is part of the real property.

C. The greenhouse cannot be part of the real property if Marta does not own the land.

B. The greenhouse is not part of the real property because it could be removed.

D. The greenhouse is a fixture and is part of the real property.

A. The greenhouse is not part of the real property because it was pre-assembled.

The current price of a non-dividend-paying stock is $32.59 and you expect the stock price to either go up by a factor of 1.397 or down by a factor of 0.716 over the next 0.7 years.

A European put option on the stock has a strike price of $33 and expires in 0.7 years. The risk-free rate is 3% (annual, continuously compounded).

Part 1. What is the option payoff if the stock price goes down?

Part 2. What is the risk-neutral probability of an up movement?

Part 3. What is the value of the option?