## All Weeks Modeling Risk and Realities Coursera Quiz Answers

### Modeling Risk and Realities Week 01 Quiz Answers

Q1. This question relates to the Hudson Readers Example discussed in Sessions 1 and 2, and assumes that the value of the advertising budget is equal to $195 million. You may use the file Hudson Readers.xlsx developed in Session 2 to answer this question.

Consider the following spending allocation of the advertising budget: A_{SI} = 60, A_{SC} = 20, A_{EI} = 0, A_{EC} = 115. What is the total net sales increase (in $ millions) corresponding to this budget allocation? Choose the closest value among the ones presented below.

- 6.85
**7.25**- 5.70
- 6.80
- 6.25

Q2. This question relates to the Hudson Readers Example discussed in Sessions 1 and 2, and assumes that the value of the advertising budget is equal to $195 million. You may use the file Hudson Readers.xlsx developed in Session 2 to answer this question.

Consider the following two ways to allocate the advertising budget:

(S1) A_{SI} = 60, A_{SC} = 22, A_{EI} = 3, A_{EC} = 110

(S2) A_{SI} = 55, A_{SC} = 10, A_{EI} = 15, A_{EC} = 115

Which of the following statements is correct:* *

- Both S1 and S2 are feasible
- S1 is infeasible, and S2 is feasible
**S1 is feasible, and S2 is infeasible**- Both S1 and S2 are infeasible

Q3. This question relates to the Hudson Readers Example discussed in Sessions 1 and 2, and assumes that the value of the advertising budget is equal to $195 million. You may use the file Hudson Readers.xlsx developed in Session 2 to answer this question.

Consider a version of the Hudson Readers Problem where the only constraints are the advertising budget constraint and the non-negativity constraints on the decision variables (in other words, ignore the constraints for net sales increase in India and China and on the net sales increase of the enhanced version). What is the optimal value of the total net sales increase (in $ millions) for such a problem? Choose the closest value among the ones presented below.* *

- 7.80
- 3.90
**9.75**- 9.25
- 5.85

Q4. This question relates to the Hudson Readers Example discussed in Sessions 1 and 2, and assumes that the value of the advertising budget is equal to $195 million. You may use the file Hudson Readers.xlsx developed in Session 2 to answer this question.

Ignore the setting of Q3 and consider the original problem formulation. One of the senior managers at the Hudson Readers believes that the constraint on the net sales increase for the enhanced version severely limits company’s ability to generate the total net sales increase. Suppose that this constraint is ignored, while all other constraints in the original problem formulation remain unchanged. Which of the following statements describes the optimal advertising spending plan in the absence of this constraint?

- The total optimal amount of advertising spending in India is 0
- The total optimal amount of advertising spending in China is 0
**The total optimal amount of advertising spending on the enhanced product is 0**- The total optimal amount of advertising spending on the standard product is 0

Q5. This question relates to the Hudson Readers Example discussed in Sessions 1 and 2, and assumes that the value of the advertising budget is equal to $195 million. You may use the file Hudson Readers.xlsx developed in Session 2 to answer this question.

Ignore the settings of Q3 and Q4 and consider the original problem formulation. Suppose that the company decides to change the requirement on the minimum net sales increase in China from the current value of $4 million to $3 million. The other constraints remain unchanged. What is the new value of the optimal total net sales increase, in $ millions? Choose the closest value among the ones below.* *

- 3.14
- 9.56
**3.00**- 7.52
- 7.38
- 9.15

Q6. This question relates to the Hudson Readers Example discussed in Sessions 1 and 2, and assumes that the value of the advertising budget is equal to $195 million. This question tests your understanding of the algebraic model formulation and does not require Excel.

The Hudson Readers is considering imposing the following additional requirement: the total amount of advertising spending in India must be at least 55 percent of the total amount of advertising spending in China. In terms of the problem’s decision variables, which algebraic expression represents this requirement?

- A
_{SC}+ A_{EC}≥ 0.55*(A_{SI }+ A_{EI}) **A**_{SI}+ A_{EI}≥ 0.55*(A_{SC }+ A_{EC})- A
_{SI}+ A_{SC}≥ 0.55*(A_{EI }+ A_{EC}) - A
_{EI}+ A_{EC}≥ 0.55*(A_{SI }+ A_{SC})

Q7. This question relates to the Epsilon Delta Capital example introduced in Session 3, and assumes that the value of the investment budget is equal to $125 million. You may use the file Epsilon Delta Capital.xlsx developed in Session 3 to answer this question.

Suppose that the Epsilon Delta Capital invests equal amount, $31.25 million, into each of the four groups of financial products. What is weighted quality score of such investment? Choose the closest among the values below.

- 2.75
- 2.00
- 2.25
- 3.00
**2.50**- 1.75

Q8. This question relates to the Epsilon Delta Capital example introduced in Session 3, and assumes that the value of the investment budget is equal to $125 million. You may use the file Epsilon Delta Capital.xlsx developed in Session 3 to answer this question.

Is the equal-amount investment of Q7 feasible for the Epsilon Delta Capital problem?

- No
**Yes**- Impossible to say

Q9. This question relates to the Epsilon Delta Capital example introduced in Session 3, and assumes that the value of the investment budget is equal to $125 million. You may use the file Epsilon Delta Capital.xlsx developed in Session 3 to answer this question.

For the equal-amount investment of Q7, what is the expected annual return, in $ millions? Choose the closest among the values below.

- 6.23
- 4.25
- 6.76
**5.31**- 5.23
- 4.03

Q10. This question relates to the Epsilon Delta Capital example introduced in Session 3, and assumes that the value of the investment budget is equal to $125 million. You may use the file Epsilon Delta Capital.xlsx developed in Session 3 to answer this question.

The** **Epsilon Delta Capital considers dropping the minimum investment requirement of $20 million on all product groups. If this requirement is removed from the Epsilon Delta Capital model, and the rest of the model remains unchanged, what is the new optimal expected return, in $ millions? Choose the closest among the values below.

- 6.46
**6.66**- 6.56
- 6.36
- 6.16
- 6.26

### Modeling Risk and Realities Week 02 Quiz Answers

Q1. This question relates to content of Session 1 and is based on the following example. Consider a model for describing a random return on Stock C next week, R_{C}. According to this model, R_{C} can be described using the following 5 scenarios. You can find these data in the posted file Stock C.xlsx.

Scenario | RC Value | Probability of Scenario |

1 | -0.01 | 0.1 |

2 | -0.03 | 0.2 |

3 | 0.01 | 0.4 |

4 | 0.02 | 0.2 |

5 | 0.04 | 0.1 |

What is the expected value of the return on Stock C next week, i.e., what is the value of E[**R _{C}**]? Choose the closest from the answers below.

- 0.000
- 0.015
- 0.010
**.005**- -0.005
- 0.020

Q2. This question relates to content of Session 1 and is based on the following example. Consider a model for describing a random return on Stock C next week, R_{C}. According to this model, R_{C} can be described using the following 5 scenarios. You can find these data in the posted file Stock C.xlsx.

Scenario | RC Value | Probability of Scenario |

1 | -0.01 | 0.1 |

2 | -0.03 | 0.2 |

3 | 0.01 | 0.4 |

4 | 0.02 | 0.2 |

5 | 0.04 | 0.1 |

What is the standard deviation of the return on Stock C next week, i.e., what is the value of SD[**R _{C}**]? Choose the closest from the answers below.

- 0.031
- 0.021
- 0.011
**0.041**- 0.051

Q3. This question relates to content of Session 1 and is based on the following example. Consider a model for describing a random return on Stock C next week, R_{C}. According to this model, R_{C} can be described using the following 5 scenarios. You can find these data in the posted file Stock C.xlsx.

Scenario | RC Value | Probability of Scenario |

1 | -0.01 | 0.1 |

2 | -0.03 | 0.2 |

3 | 0.01 | 0.4 |

4 | 0.02 | 0.2 |

5 | 0.04 | 0.1 |

What is the probability that the return on Stock C next week is negative? Choose the closest from the answers below.

- 0.2
**0.5**- 0.1
- 0.3
- 0.4

Q4. This question relates to content of Sessions 1 and 2 and is based on the following example. Consider a model for describing random returns on Stocks D and E next week, R_{D} and R_{E}. According to this model, R_{D} and R_{E} can be described using the following 3 scenarios. You can find these data in the posted file Stocks DE.xlsx.

Scenario | ValueR_{D} | ValueR_{E} | Probability of Scenario |

1 | -0.04 | 0.01 | 0.3 |

2 | 0.03 | 0.02 | 0.5 |

3 | 0.01 | -0.005 | 0.2 |

Let E[**R _{D}**] and E[

**R**] be the expected return values for Stocks D and E next week, respectively, and let SD[

_{E}**R**] and SD[

_{D}**R**] be the standard deviations of the returns for Stocks D and E next week, respectively. Which of the following statements is correct?

_{E}- E[
**R**] > E[_{D}**R**] and SD[_{E}**R**] > SD[_{D}**R**]_{E} - E[
**R**] ≤ E[_{D}**R**] and SD[_{E}**R**] ≤ SD[_{D}**R**]_{E} **E[R**_{D}] > E[R_{E}] and SD[R_{D}] ≤ SD[R_{E}]- E[
**R**] ≤ E[_{D}**R**] and SD[_{E}**R**] > SD[_{D}**R**]_{E}

Q5. This question relates to content of Sessions 1 and 2 and is based on the following example. Consider a model for describing random returns on Stocks D and E next week, R_{D} and R_{E}. According to this model, R_{D} and R_{E} can be described using the following 3 scenarios. You can find these data in the posted file Stocks DE.xlsx.

Scenario | ValueR_{D} | ValueR_{E} | Probability of Scenario |

1 | -0.04 | 0.01 | 0.3 |

2 | 0.03 | 0.02 | 0.5 |

3 | 0.01 | -0.005 | 0.2 |

What is the value of the correlation coefficient between **R _{D}** and

**R**? Choose the closest answer from the ones presented below.

_{E}- 0
- 1
- -1
- -0.379
- -0.165
**0.165**- 0.379

Q6. This question relates to content of Sessions 1 and 2 and is based on the following example. Consider a model for describing random returns on Stocks D and E next week, R_{D} and R_{E}. According to this model, R_{D} and R_{E} can be described using the following 3 scenarios. You can find these data in the posted file Stocks DE.xlsx.

Scenario | ValueR_{D} | ValueR_{E} | Probability of Scenario |

1 | -0.04 | 0.01 | 0.3 |

2 | 0.03 | 0.02 | 0.5 |

3 | 0.01 | -0.005 | 0.2 |

Suppose that a financial company invests $100,000 in the Stock D and $200,000 in the Stock E now. What is the highest possible value of profit, in $, associated with this investment that the company can earn next week? Choose the closest answer from the ones presented below.

**7000**- 5000
- -2000
- 0
- 2000

Q7. This question relates to content of Sessions 1 and 2 and is based on the following example. Consider a model for describing random returns on Stocks D and E next week, R_{D} and R_{E}. According to this model, R_{D} and R_{E} can be described using the following 3 scenarios. You can find these data in the posted file Stocks DE.xlsx.

Scenario | ValueR_{D} | ValueR_{E} | Probability of Scenario |

1 | -0.04 | 0.01 | 0.3 |

2 | 0.03 | 0.02 | 0.5 |

3 | 0.01 | -0.005 | 0.2 |

Under the investment plan of Q6, what is the expected value of profit, in $, that the company will earn next week? Choose the closest answer from the ones presented below.

- 3400
- 2900
- 0
**1700**- 2200

Q8. This question relates to the two-stock example considered in Session 3. In answering these questions, you can use the Excel file TwoStocks_Solved.xlsx.

Suppose that an investor is considering a portfolio with X_{A }=75,000, X_{B }= 25,000. In other words, the investor decides to put $75,000 in the Stock A and $25,000 in the Stock B “today”. What is the expected profit, in $, such a portfolio will earn tomorrow? Choose the closest answer from the ones presented below.

- 284
- 96
- 159
- 222
**347**

Q9. This question relates to the two-stock example considered in Session 3. In answering these questions, you can use the Excel file TwoStocks_Solved.xlsx.

What is the value of the standard deviation of profits, in $, for the portfolio considered in Q8? Choose the closest answer from the ones presented below.

**1344**- 1446
- 1808
- 2030
- 2809

Q10. This question relates to the two-stock example considered in Session 3. In answering these questions, you can use the Excel file TwoStocks_Solved.xlsx.

Suppose that an investor would like to split $100,000 between Stocks A and Stock B “today” so as to maximize the expected profit “tomorrow” irrespective of the standard deviation of the resulting profit. In other words, suppose that the investor “drops” the constraint on the maximum allowable value of the standard deviation of profits, while keeping the rest of the constraints in the portfolio problem. Which of the following choices describes the optimal portfolio in this case?

- X
_{A }= 0, X_{B }= 100,000 - X
_{A }=100,000, X_{B }= 0 **X**_{A }=25,000, X_{B }= 75,000- X
_{A }= 50,000, X_{B }= 50,000 - X
_{A }=75,000, X_{B }= 25,000

### Modeling Risk and Realities Week 03 Quiz Answers

Q1. A sports team named Philadelphia Streets has a probability of (2/3) for winning each game against their division rivals Hockeytown. They play 12 games against each other during the season. Assume that the outcome of any particular game is independent from an outcome of any other game. Let X be the random variable that stands for the number of wins that Philadelphia Streets will have in those 12 games. What is the expected value of X?

- 8
- 6
**12**- 4
- 10

Q2. Re-examine the medical drug success example in the videos. Recall that the number of the successes is distributed binomially (i.e., according to a binomial distribution).

Based on the definition of the mode, what is the mode of the distribution of successes? (Recall that the mode is the most likely value that a random variable can take).

- 4
- 8
- 6
- 12
**10**

Q3. The number of shares of a stock traded during a day for a firm is approximated by a random variable that is normally distributed with mean 3192 and standard deviation 1181.

What is the probability that the number of shares traded is less than or equal to 4200?

- 0.50
**0.9998**- 0.20
- 0.0002
- 0.002
- 0.80

Q4. **The number of shares of a stock traded during a day for a firm is approximated by a random variable that is normally distributed with mean 3192 and standard deviation 1181.**

Calculate the pdf value at x=3200.

- 0.202
- 0.9997
- 0.502
**0.0003**- 0.003
- 0.801

Q5. **The forecast monthly revenues for a firm are modeled using a random variable that is distributed according to a normal distribution with mean $850,000 and standard deviation $165,000.**

What is median value of this distribution, in $?

- 520,000
- 200,000
**685,000**- 1,015,000
- 850,000
- 1,180,000

Q6. **The forecast monthly revenues for a firm are modeled using a random variable that is distributed according to a normal distribution with mean $850,000 and standard deviation $165,000.**

What is the probability that the revenues will be less than $700,000? Choose the closest numerical answer.

- 0.27
- 0.10
- 0.82
**0.18**- 0.73
- 0.50
- 0.90

Q7. **The forecast monthly revenues for a firm are modeled using a random variable that is distributed according to a normal distribution with mean $850,000 and standard deviation $165,000.**

What is the probability that revenues will exceed 1 million dollars? Choose the closest answer.

- 0.18
**0.73**- 0.90
- 0.82
- 0.27
- 0.10
- 0.50

Q8. **A financial advisor at a financial consulting firm spends time with his investing clients throughout the year. Based on the historical data, he finds that the consulting time T spent with a client can be modeled as a continuous, uniformly distributed random variable, with the minimum value of 50 minutes and the maximum value of 183 minutes.**

What is the pdf value of this distribution at T=67 minutes?

**0.9825**- 0.47
- 0.33
- 0.0075
- 0.53
- 0.67

Q9. A financial advisor at a financial consulting firm spends time with his investing clients throughout the year. Based on the historical data, he finds that the consulting time T spent with a client can be modeled as a continuous, uniformly distributed random variable, with the minimum value of 50 minutes and the maximum value of 183 minutes.

What is the probability that his consulting time with an investor client will not exceed 2 hours (i.e., 120 minutes)? Choose the closest answer.

- 0.33
- 0.53
**0.0075**- 0.67
- 0.47
- 0.9825

Q10. Suppose you are working on a project based on some complex data from your firm. You have broken down the 1344 data points that you have into 35 buckets or bins. You are now testing the goodness of fit, using a chi-square test for a distribution that is characterized by 3 parameters.

What is the number of degrees of freedom associated with your chi-square test?

- 35
- 31
- 7
- 3
- 1340
- 2
**1344**- 32

### Modeling Risk and Realities Week 04 Quiz Answers

Q1. All questions in this quiz relate to the Stargrove example covered during this week. You can use the file Stargrove.xlsx to answer these questions. In this question, we assume that the Stargrove decides to build R=96 regular and L=12 luxury apartments.

Suppose that the demand for regular apartments turns out to be D_{R} = 94. How much profit, in $ millions, will the company earn from the sales of regular apartments, including the sales at the $500,000 profit margin as well as the sales at the $100,000 profit margin? Note that you should not count the profit from the sales of luxury apartments. Choose the closest from the answers below.

- 47.2
**48.2**- 48
- 51.6
- 47

Q2. All questions in this quiz relate to the Stargrove example covered during this week. You can use the file Stargrove.xlsx to answer these questions. In this question, we assume that the Stargrove decides to build R=96 regular and L=12 luxury apartments.

What is maximum amount of profit, in $ millions, that the company can earn from the sales of regular apartments, including the sales at the $500,000 profit margin as well as the sales at the $100,000 profit margin? Note that you should not count the profit from the sales of luxury apartments. Choose the closest from the answers below.* *

- 47.2
- 48
- 48.2
**51.6**- 47

Q3. All questions in this quiz relate to the Stargrove example covered during this week. You can use the file Stargrove.xlsx to answer these questions. In this question, we assume that the Stargrove decides to build R=96 regular and L=12 luxury apartments.

Suppose that the actual demand for regular apartments at the $500,000 profit margin, D_{R}, is such that the Stargrove realized a profit of $500,000 from selling regular apartments to the real estate investment company at the salvage profit margin of $100,000 per apartment. How much profit, in $ millions, did the Stargrove earn from the sales of the remaining regular apartments at the $500,000 profit margin for the same realization of demand D_{R}? Choose the closest from the answers below.

- 45.5
- 45
- 45.2
- 46
**46.2**- 46.5

Q4. All questions in this quiz relate to the Stargrove example covered during this week. You can use the file Stargrove.xlsx to answer these questions. In this question, we assume that the Stargrove decides to build R=96 regular and L=12 luxury apartments.

For what value of the demand for regular apartments, D_{R}, the profit from selling regular apartments at the high profit margin of $500,000 is equal to the profit of selling regular apartments to real estate investment company at the salvage profit margin of $100,000?

- 6
- 36
- 16
**26**- 46

Q5. All questions in this quiz relate to the Stargrove example covered during this week. You can use the file Stargrove.xlsx to answer these questions. In this question, we assume that the Stargrove decides to build R=96 regular and L=12 luxury apartments.

Suppose that we have set up a simulation with *n*=4 simulation runs that generated the following random instances for the demand for regular apartments, D_{R}: 88, 91, 97, and 103. Calculate the four corresponding values of the profit from the sales of regular apartments (i.e., the sum of profits at both the high profit margin of $500,000 and the low profit margin of $100,000) and use Excel to generate the descriptive statistics for this sample of four profit values. What is the sample mean, in millions of $, of these four profit values? Choose the closest from the answers below.

- 42.7
- 43.7
**45.7**- 44.7
- 46.7

Q6. All questions in this quiz relate to the Stargrove example covered during this week. You can use the file Stargrove.xlsx to answer these questions. In this question, we assume that the Stargrove decides to build R=96 regular and L=12 luxury apartments.

Suppose that the same simulation as in Q5 generated the following random instances for the demand for luxury apartments, D_{L}: 5, 7, 12, and 13. Calculate the four corresponding values of the profit from the sales of luxury apartments (i.e., the sum of profits at both the high profit margin of $900,000 and the low profit margin of $150,000) and use Excel to generate the descriptive statistics for this sample of four profit values. What is the sample standard deviation, in millions of $, of these four profit values? Choose the closest from the answers below.

- 4.7
**2.7**- 1.7
- 5.7
- 3.7

Q7. All questions in this quiz relate to the Stargrove example covered during this week. You can use the file Stargrove.xlsx to answer these questions. In this question, we assume that the Stargrove decides to build R=96 regular and L=12 luxury apartments.

Using four random instances of the demand for regular apartments from Q5 and four random instances of the demand for luxury apartments from Q6, calculate the four corresponding total profit values obtained from sales of both regular and luxury apartments. Based on this four values, estimate the likelihood of the total profit to be above $52 million. Choose the closest from the answers below.

- 0.75
- 0.1
**0.25**- 0.5
- 0.9

Q8. All questions in this quiz relate to the Stargrove example covered during this week. You can use the file Stargrove.xlsx to answer these questions. In this question, we assume that the Stargrove decides to build R=96 regular and L=12 luxury apartments.

Use Excel to generate descriptive statistics for the four profit values in Q7 and calculate the 95% confidence interval for the true expected value of the total profit. If this interval has the form [$X, $Y], what is the value of X, expressed in millions? Choose the closest from the answers below.

**48.5**- 6.8
- 2.1
- 62
- 55.3

Q9. All questions in this quiz relate to the Stargrove example covered during this week. You can use the file Stargrove.xlsx to answer these questions. This question is focused on an alternative decision to build R=88 regular and L=16 luxury apartments.

Consider the decision to build R=88 regular and L=16 luxury apartments. Using the four random instances of the demand for regular apartments from Q5 and four random instances of the demand for luxury apartments from Q6, calculate the four corresponding total profit values obtained from sales of both regular and luxury apartments under this decision. Based on this four values, estimate the likelihood of the total profit to be above $52 million. Choose the closest from the answers below.* *

- 0.9
**0.75**- .5
- 0.25
- 0.1

Q10. All questions in this quiz relate to the Stargrove example covered during this week. You can use the file Stargrove.xlsx to answer these questions. This question is focused on an alternative decision to build R=88 regular and L=16 luxury apartments.

Use Excel to generate descriptive statistics for the four profit values in Q9 and calculate the 95% confidence interval for the true expected value of the total profit. If this interval has the form [$N, $M], what is the value of M-N, i.e., what is width of the 95% confidence interval for the expected value of the total profit? Express the value in millions and choose the closest from the answers below.

- 1.4
**2.9**- 9.2
- 4.6

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