1)Which of the following are correct statements about the Bellman Equation?

A) Bellman equation represents the value of a state in terms of the value of successor states.

B) Bellman equation represents the expected value of successor states.

C) Bellman equation can be written for a state or a state-action pair.

D) Bellman equation is based on an approximation of the value of the current state.

2) Which of the following describes what a backup diagram represents? (Please explain)

a)Shows the current state and all possible subsequent actions and states, and the expected value of a state can be computed by ‘backing-up’ over the values of subsequent states in the diagram.

b)Shows all possible paths to arrive at the current state, and can be used to compute the expected values of the predecessor states by ‘backing up’ over the values of these predecessor states.

c)Shows all possible paths to arrive at the current state, and can be used to compute the expected values of the current state by ‘backing up over the state values in the diagram.

d)Shows the current state and all possible subsequent actions and states, and the expected value of a predecessor state can be computed by ‘backing-up’ over the values of the states in the diagram.

Are Southern and Western states equally prone to fatal lightning strikes? Suppose the number of lightning strike fatalities over a 5-year period for Southern and Western states are shown as follows.

Use α = 0.05 and test to determine whether the distribution of lightning fatalities is the same for these two regions.

State the null and alternative hypotheses.

H₀: The two populations of lightning fatalities are identical.
H_a: The two populations of lightning fatalities are not identical.H₀: Median number of lightning fatalities for Southern states − Median number of lightning fatalities for Western states > 0
H_a: Median number of lightning fatalities for Southern states − Median number of lightning fatalities for Western states = 0    H₀: Median number of lightning fatalities for Southern states − Median number of lightning fatalities for Western states ≤ 0
H_a: Median number of lightning fatalities for Southern states − Median number of lightning fatalities for Western states > 0H₀: Median number of lightning fatalities for Southern states − Median number of lightning fatalities for Western states ≥ 0
H_a: Median number of lightning fatalities for Southern states − Median number of lightning fatalities for Western states < 0H₀: The two populations of lightning fatalities are not identical.
H_a: The two populations of lightning fatalities are identical.

Find the value of the test statistic.

W =

Find the p-value. (Round your answer to four decimal places.)

p-value =

What is your conclusion?

Do not reject H₀. There is sufficient evidence to conclude that the distribution of lightning fatalities is different for these two regions.Reject H₀. There is sufficient evidence to conclude that the distribution of lightning fatalities is different for these two regions.    Reject H₀. There is not sufficient evidence to conclude that the distribution of lightning fatalities is different for these two regions.Do not reject H₀. There is not sufficient evidence to conclude that the distribution of lightning fatalities is different for these two regions.

Are Southern and Western states equally prone to fatal lightning strikes? Suppose the number of lightning strike fatalities over a 5-year period for Southern and Western states are shown as follows.

Use α = 0.05 and test to determine whether the distribution of lightning fatalities is the same for these two regions.

State the null and alternative hypotheses.

H₀: Median number of lightning fatalities for Southern states − Median number of lightning fatalities for Western states ≥ 0
H_a: Median number of lightning fatalities for Southern states − Median number of lightning fatalities for Western states < 0

H₀: The two populations of lightning fatalities are identical.
H_a: The two populations of lightning fatalities are not identical.    

H₀: The two populations of lightning fatalities are not identical.
H_a: The two populations of lightning fatalities are identical.

H₀: Median number of lightning fatalities for Southern states − Median number of lightning fatalities for Western states ≤ 0
H_a: Median number of lightning fatalities for Southern states − Median number of lightning fatalities for Western states > 0

H₀: Median number of lightning fatalities for Southern states − Median number of lightning fatalities for Western states > 0
H_a: Median number of lightning fatalities for Southern states − Median number of lightning fatalities for Western states = 0

Find the value of the test statistic.

W =

Find the p-value. (Round your answer to four decimal places.)

p-value =

What is your conclusion?

Reject H₀. There is sufficient evidence to conclude that the distribution of lightning fatalities is different for these two regions.

Do not reject H₀. There is not sufficient evidence to conclude that the distribution of lightning fatalities is different for these two regions.    

Reject H₀. There is not sufficient evidence to conclude that the distribution of lightning fatalities is different for these two regions.

Do not reject H₀. There is sufficient evidence to conclude that the distribution of lightning fatalities is different for these two regions.

2. Joanne Jamison

Joanne started with Performance Horizons five years ago, after receiving her MBA from The Wharton School. She has told people the reason she went to Wharton was to have the best opportunities at jobs that would offer quick advancement so she could rapidly rise to the top of the organization. Joanne has a keen sense of what makes organizations tick and who to go to when things need to get done. She doesn’t “waste” her time with chitchat, as she calls it. Her time is all spent on doing a good job on all her assignments and making sure she makes the right connections with the executives. Her performance has always been rated as excellent.

Which two of the four motivates Joanne the most?

Business Week conducted a survey of graduates from 30 top MBA programs (Business Week, September 22, 2003). The survey found that the average annual salary for male and female graduates 10 years after graduation was $168,000 and $117,000, respectively. Assume the population standard deviation for the male graduates is $40,000, and for the female graduates it is $25,000.

When calculating values for z, round to two decimal places.

1. What is the probability that a simple random sample of 40 male graduates will provide a sample mean within $10,000 of the population mean, $168,000 (to 4 decimals)?
   
   
2. What is the probability that a simple random sample of 40 female graduates will provide a sample mean within $10,000 of the population mean, $117,000 (to 4 decimals)?
   
   
3. In which of the preceding two cases, part (a) or part (b), do we have a higher probability of obtaining a sample estimate within $10,000 of the population mean?
   - Select your answer -Part (a) because the population mean for males is higherPart (a) because the population standard deviation for males is higherPart (b) because the population mean for females is lowerPart (b) because the population standard deviation for females is lowerItem 3
   
4. What is the probability that a simple random sample of 100 male graduates will provide a sample mean more than $4,000 below the population mean (to 4 decimals)?

Artie Siegel, an MBA student, has been having problems balancing his checkbook. His monthly income is derived from a graduate research assistantship; however, he also makes extra money in most months by tutoring undergraduates in their quantitative analysis course. His historical chances of various income levels are shown in the following table: Monthly Income* ($) Probability 350 0.40 400 0.20 450 0.30 500 0.10 *Assume that this income is received at the beginning of each month. Siegel’s expenditures also vary from month to month, and he estimates that they will follow this distribution: Monthly Expenses ($) Probability 300 0.10 400 0.45 500 0.30 600 0.15 He begins his final year with $600 in his checking account. Simulate the entire year (12 months) on the next page and discuss Siegel’s financial picture, i.e., will he be able to keep his head above water--(out of debt)? What is his expected average profit for the 12 months? Use the random numbers below. Random numbers for Income and Expenses Income .85 .54 .73 .95 .9 .19 .81 .2 .76 .55 .57 .01 Expenses .99 .44 .01 .80 .95 .72 .75 .16 .32 .57 .31 .32

Please complete in excel and attached excel screenshot! Much appreciated!

After graduating from college with your MBA, you decide to take your grandma’s secret cinnamon roll recipe and open up a bakery. You grew up devouring your grandma’s rolls, and you have convinced her to give you the secret. You are confident that your bakery will be the next big hit in the fast-food business. You take out a business loan for the maximum amount your bank will give you, hire several employees, and open a beautiful store that is designed to look like your grandma’s home. After eight months of hard work and diligence, you are crushed when you realize that your store manager has been stealing from you. One of your recent hires tells you that during her last shift, the manager, Stephanie, voided a sale of two-dozen cinnamon rolls, stamped the receipt as a return, and pocketed the money. Stephanie warned the new hire not to say anything and told her she deserved the money because she didn’t get paid enough. Encouraged by your open- door policy, the employee confides in you.

1. Identify what symptoms this fraud will generate. In addition, identify how this fraud will directly affect your revenue and inventory accounts.

2. Explain the steps you should take to search for each symptom you identified in part (1). In particular, describe the computer queries and transactions that should be searched to find this fraud.

3. After you have identified several symptoms, do you have enough evidence to prove that she is guilty? What other evidence is required or useful in this case?

4. Besides searching for symptoms of the fraud, what other investigative steps can be taken to elicit a confession or otherwise prove the fraud?

5. What steps could have been taken to prevent this fraud from occurring in the first place?

Sheila Goodman recently received her MBA from the Harvard Business School. She has joined the family business, Goodman Software Products Inc., as Vice-President of Finance. She believes in adjusting projects for risk. Her father is somewhat skeptical but agrees to go along with her. Her approach is somewhat different than the risk-adjusted discount rate approach, but achieves the same objective. She suggests that the inflows for each year of a project be adjusted downward for lack of certainty and then be discounted back at a risk-free rate. The theory is that the adjustment penalty makes the inflows the equivalent of riskless inflows, and therefore a risk-free rate is justified.

A table showing the possible coefficient of variation for an inflow and the associated adjustment factor is shown next:
  

Assume a $125,000 project provides the following inflows with the associated coefficients of variation for each year.
  

  
Use Appendix B for an approximate answer but calculate your final answer using the formula and financial calculator methods.

a. Fill in the table below: (Do not round intermediate calculations. Round "Adjustment Factor" answers to 2 decimal places and other answers to the nearest whole dollar.)
  

  
b-1. If the risk-free rate is 6 percent, compute the net present value of the adjusted inflows. (Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places.)
  

Sheila Goodman recently received her MBA from the Harvard Business School. She has joined the family business, Goodman Software Products Inc., as Vice-President of Finance. She believes in adjusting projects for risk. Her father is somewhat skeptical but agrees to go along with her. Her approach is somewhat different than the risk-adjusted discount rate approach, but achieves the same objective. She suggests that the inflows for each year of a project be adjusted downward for lack of certainty and then be discounted back at a risk-free rate. The theory is that the adjustment penalty makes the inflows the equivalent of riskless inflows, and therefore a risk-free rate is justified.

A table showing the possible coefficient of variation for an inflow and the associated adjustment factor is shown next:
  

Assume a $185,000 project provides the following inflows with the associated coefficients of variation for each year.
  

  
Use Appendix B for an approximate answer but calculate your final answer using the formula and financial calculator methods.

a. Fill in the table below: (Do not round intermediate calculations. Round "Adjustment Factor" answers to 2 decimal places and other answers to the nearest whole dollar.)
  

  
b-1. If the risk-free rate is 7 percent, compute the net present value of the adjusted inflows. (Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places.)
  

  
b-2. Should this project be accepted?
  

• Yes

• No