Questions
A financial institution has the following portfolio of over-the-counter options on sterling: Type Position Delta of...

A financial institution has the following portfolio of over-the-counter options on sterling:

Type

Position

Delta of Option

Gamma of Option

Vega of Option

Call

-2,000

0.5

2.2

1.8

Call

-1000

0.8

0.6

0.2

Put

-4,000

-0.40

1.3

0.7

Call

-1000

0.70

1.8

1.4

A traded option is available with a delta of 0.6, a gamma of 1.5, and a vega of 0.8.

Is it possible to find a position in the traded option and in sterling that make the portfolio gamma neutral, vega neutral and delta neutral? Explain.        

In: Finance

A financial institution has the following portfolio of over-the-counter options on sterling: Type, Position, Delta of...

A financial institution has the following portfolio of over-the-counter options on sterling: Type, Position, Delta of Option, Gamma of Option, Vega of Option ,Call -2,000 ,0.5, 2.2, 1.8; Call -1000, 0.8, 0.6 ,0.2 ;Put -4,000 ,-0.40, 1.3, 0.7 ;Call -1000 ,0.70, 1.8, 1.4;

A traded option is available with a delta of 0.6, a gamma of 1.5, and a vega of 0.8.

a. Is it possible to find a position in the traded option and in sterling that make the portfolio gamma neutral, vega neutral and delta neutral? Explain.

In: Finance

Recent research indicates that the effectiveness of antidepressant medication is directly related to the severity of...

Recent research indicates that the effectiveness of antidepressant medication is directly related to the severity of the depression (Khan, Brodhead, Kolts & Brown, 2005). Based on pretreatment depression scores, patients were divided into four groups based on their level of depression. After receiving the antidepressant medication, depression scores were measured again and the amount of improvement was recorded for each patient. The following data are similar to the results of the study.

Low
Moderate
High
Moderate
Moderately
Severe

Severe
3.3 0.7 2 2.8
0 2.7 2.3 3.2
3.2 4 1.1 1.9
2.6 1.4 1 4.2
0.8 2.8 2.7 1.4
2.9 2.5 3.3 1.7
1.1 0 1.8 1.1
2.9 2.6 1.8 3.2
4.5 2 4.7 3.5
1.6 0.3 1.5 1.5
3.3 1.6 0.7 3.4
1 1.5 3 3.2
0.6 2.2 1.8 2.1
2.3 2.6 2.7 1.4
3.7 1.9 1.1 2.1
2.8 4.7 1.9 1.5
1.7 1.2 1.5 2.6
1.6 0.9 0 4.1
1.8 3.4 1.4 3.6
2.1 2 1.4 2.3
2.1 0.2 2.4 0.7
2.4 1.1 2.1 1.9
3.3 3.4 2.2 2.4
0.1 0.3 2.2 2.6
4.5 2.5 1.1 3.5
2.6 1.9 3.7 3.1
2.7 1.3 3.1 2.5
1.9 2.5 1.1 2.6
1.7 2 1.7 3.8
1.3 2.5 2.9 2.5
1.5 1.5 2.2 3.3
2.5 4.2 1.6 3.2
4.2 3.3 2.1 3.4
2.1 1.4 3.3 2.1
1.5 2.7 0.4 1.5
1.2 3 1.4 1.5
1.9 1 1.7 3.8
1.1 1.5 2.8 2.6
3.4 1.5 1.5 1.1
1.2 2.5 1.3 2.5
3.5 1.8 0 1.9
1.1 3.7 0.2 2.5
2.8 1.5 0.9 2.5
1.2 0.7 3.7 0
1.1 1.5 1.3 3.4
3.2 2.5 2.7 1.9
0.3 1.2 1.3 3.1
0.4 1.9 3.8 2.1
1.6 2.8 2.5 4.1
2.2 2.2 2 4.1
3.5 2.6 0.3 2.1
2 3.9 4 3.8
2.4 1.6 2 4.1
0 1.3 1.4 3.6
3.7 2 2.8 2.5
0.8 1.5 2.4 1.5
4.4 0.5 2.2 3.2
2.8 2.1 1.8 1.5
3 3.1 2.4 1.8
1.6 0.7 1 2.6
1.7 1.8 3.7 3.9

This is the summary table for the ANOVA test:

S.S. d.f. M.S.
Between 14.348360655737 3 4.7827868852458
Within 260.6737704918 240 1.0861407103825
TOTAL 275.02213114754 243

From this table, you obtain the necessary statistics for the ANOVA:
F-ratio: 4.4034689424001
p-value: 0.00489
η2=η2= 0.052171658316617

What is your final conclusion? Use a significance level of α=0.02α=0.02.

  • There is a significant difference between treatments
  • These data do not provide evidence of a difference between the treatments

Explain what this tells us about the equality of mean?

Let's look at the boxplot for each treatment:

012345Depression ScoresLow ModerateHigh ModerateModerately SevereSevere

How could boxplots refine our conclusion in an ANOVA test? Your answer should address this specific problem.

Edit

Insert

Formats

In: Statistics and Probability

Recent research indicates that the effectiveness of antidepressant medication is directly related to the severity of...

Recent research indicates that the effectiveness of antidepressant medication is directly related to the severity of the depression (Khan, Brodhead, Kolts & Brown, 2005). Based on pretreatment depression scores, patients were divided into four groups based on their level of depression. After receiving the antidepressant medication, depression scores were measured again and the amount of improvement was recorded for each patient. The following data are similar to the results of the study.

Low
Moderate
High
Moderate
Moderately
Severe

Severe
3.3 0.7 2 2.8
0 2.7 2.3 3.2
3.2 4 1.1 1.9
2.6 1.4 1 4.2
0.8 2.8 2.7 1.4
2.9 2.5 3.3 1.7
1.1 0 1.8 1.1
2.9 2.6 1.8 3.2
4.5 2 4.7 3.5
1.6 0.3 1.5 1.5
3.3 1.6 0.7 3.4
1 1.5 3 3.2
0.6 2.2 1.8 2.1
2.3 2.6 2.7 1.4
3.7 1.9 1.1 2.1
2.8 4.7 1.9 1.5
1.7 1.2 1.5 2.6
1.6 0.9 0 4.1
1.8 3.4 1.4 3.6
2.1 2 1.4 2.3
2.1 0.2 2.4 0.7
2.4 1.1 2.1 1.9
3.3 3.4 2.2 2.4
0.1 0.3 2.2 2.6
4.5 2.5 1.1 3.5
2.6 1.9 3.7 3.1
2.7 1.3 3.1 2.5
1.9 2.5 1.1 2.6
1.7 2 1.7 3.8
1.3 2.5 2.9 2.5
1.5 1.5 2.2 3.3
2.5 4.2 1.6 3.2
4.2 3.3 2.1 3.4
2.1 1.4 3.3 2.1
1.5 2.7 0.4 1.5
1.2 3 1.4 1.5
1.9 1 1.7 3.8
1.1 1.5 2.8 2.6
3.4 1.5 1.5 1.1
1.2 2.5 1.3 2.5
3.5 1.8 0 1.9
1.1 3.7 0.2 2.5
2.8 1.5 0.9 2.5
1.2 0.7 3.7 0
1.1 1.5 1.3 3.4
3.2 2.5 2.7 1.9
0.3 1.2 1.3 3.1
0.4 1.9 3.8 2.1
1.6 2.8 2.5 4.1
2.2 2.2 2 4.1
3.5 2.6 0.3 2.1
2 3.9 4 3.8
2.4 1.6 2 4.1
0 1.3 1.4 3.6
3.7 2 2.8 2.5
0.8 1.5 2.4 1.5
4.4 0.5 2.2 3.2
2.8 2.1 1.8 1.5
3 3.1 2.4 1.8
1.6 0.7 1 2.6
1.7 1.8 3.7 3.9

This is the summary table for the ANOVA test:

S.S. d.f. M.S.
Between 14.348360655737 3 4.7827868852458
Within 260.6737704918 240 1.0861407103825
TOTAL 275.02213114754 243

From this table, you obtain the necessary statistics for the ANOVA:
F-ratio: 4.4034689424001
p-value: 0.00489
η2=η2= 0.052171658316617

What is your final conclusion? Use a significance level of α=0.02α=0.02.

  • There is a significant difference between treatments
  • These data do not provide evidence of a difference between the treatments

Explain what this tells us about the equality of mean?

Let's look at the boxplot for each treatment:

012345Depression ScoresLow ModerateHigh ModerateModerately SevereSevere

How could boxplots refine our conclusion in an ANOVA test? Your answer should address this specific problem.

Edit

Insert

Formats

In: Statistics and Probability

(1). Use the Wilcoxon matched-pairs signed rank test (small sample size) to determine whether there is...

  1. (1). Use the Wilcoxon matched-pairs signed rank test (small sample size) to determine whether there is a significant difference between the related populations represented by the matched pairs given here. Assume a = .05 (Written).

Group1

Group2

d

5.6

6.4

-0.8

1.3

1.5

-0.2

4.7

4.6

0.1

3.8

4.3

-0.5

2.4

2.1

0.3

5.5

6

-0.5

5.1

5.2

-0.1

4.6

4.5

0.1

3.7

4.5

-0.8

In: Statistics and Probability

If x is a binomial random​ variable, use the binomial probability table to find the probabilities...

If x is a binomial random​ variable, use the binomial probability table to find the probabilities below.

a. P(x=3) for n=10, p=0.5

b. P(x≤4) for n=15, p=0.3

c. P(x>1) for n=5, p=0.2

d. P(x<6) for n=15, p=0.8

e. P(x≥14) for n=25, p=0.8

f. P(x=3) for n=20, p=0.1

In: Statistics and Probability

Imagine you are a pipeline company trying to sell a new project to a shipper of...

Imagine you are a pipeline company trying to sell a new project to a shipper of oil for a new refinery.

Pipeline Length: 266 miles (16,853,760 inches)

The refinery is scheduled to take 300,000 barrels per day of Bakken Crude at typical temperatures. ​Temperature: 60 degrees Fahrenheit. Flow rate = 33687.5 in3​/s. Kinematic viscosity: 3.337 centistokes or 0.0051723603 in2​/s. Specific Gravity = 0.7

​Calculate Reynold's number.

​Friction Factor: 0.0275.

​Calculate Pressure Drop.

Pipeline flows entirely through class I locations except for 10 miles located in a class IV location. You have the option of bypassing the class IV location by running the pipeline an additional 50 miles.

Pipe Diameter: 12 inches X-42 Schedule 20

​Calculate Maximum Pressure

The inlet pressure of pumping stations should not fall below 400 psi.

Set distance between pumping stations optimally.

Calculate horsepower requirements

In: Mechanical Engineering

Question 3. - Please do c, d and e An engineer suspects that the surface finish...

Question 3. - Please do c, d and e

An engineer suspects that the surface finish of a metal part is influenced by the feed rate and the depth of cut of a particular manufacturing machine. An experiment is conducted and the data can be found in SurfaceFinish.jmp on eCampus.

a. State the two-way ANOVA model corresponding to this data. Be sure to define each term in your model and list any assumptions that are made.

b. Perform the test to determine if the model from part a) is significant.

c. Prepare a profile plot for the cell mean surface finish scores. Does it appear that any interaction effects are present? Explain.

d. Test whether or not interaction effects are present.

e. Given that low surface finish scores are desirable, which combination(s) of feed rate and depth of cut do you recommend?

Depth of Cut (in) = 0.15 0.15 0.15 0.18 0.18 0.18 0.2 0.2 0.2 0.25 0.25 0.25 0.15 0.15 0.15 0.18 0.18 0.18 0.2 0.2 0.2 0.25 0.25 0.25 0.15 0.15 0.15 0.18 0.18 0.18 0.2 0.2 0.2 0.25 0.25 0.25

Feed Rate (in/min) = 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3

Surface Finsih Score = 74 64 60 79 68 73 82 88 92 99 104 96 92 86 88 98 104 88 99 108 95 104 110 99 99 98 102 104 99 95 108 110 99 114 107 111

Depth of Cut (in) Feed Rate (in/min)   
Surface Finish Score
0.15 0.2 74
0.15 0.2 64
0.15 0.2 60
0.18 0.2 79
0.18 0.2 68
0.18 0.2 73
0.2 0.2 82
0.2 0.2 88
0.2 0.2 92
0.25 0.2 99
0.25 0.2 104
0.25 0.2 96
0.15 0.25 92
0.15 0.25 86
0.15 0.25 88
0.18 0.25 98
0.18 0.25 104
0.18 0.25 88
0.2 0.25 99
0.2 0.25 108
0.2 0.25 95
0.25 0.25 104
0.25 0.25 110
0.25 0.25 99
0.15 0.3 99
0.15 0.3 98
0.15 0.3 102
0.18 0.3 104
0.18 0.3 99
0.18 0.3 95
0.2 0.3 108
0.2 0.3 110
0.2 0.3 99
0.25 0.3 114
0.25 0.3 107
0.25 0.3 111

In: Statistics and Probability

Q4Y4 Q1Y5 Q2Y5 Q3Y5 Q4Y5 Total Budgeted Sales (Actual for Q4Y4) 10000 11000 14000 15000 17000...

Q4Y4 Q1Y5 Q2Y5 Q3Y5 Q4Y5 Total
Budgeted Sales (Actual for Q4Y4) 10000 11000 14000 15000 17000 57000
Selling Price/per unit 9 9 9 9 9 9
Sale Collection
In quarter of sale 0.8
In following quarter 0.2
Desired ending finished goods inventory 2500 2200 2400 2100 2100
Raw Materials/per unit 5 5 5 5 5 5
Desired Ending raw material inventory Inventory 5000 8000 7000 6000 5000 5000
Raw material price/per unit 2 2 2 2 2 2
Accounts payable
In quarter of purchase 0.7
In following quarter 0.3
Q4Y4 raw material cost 100000

REQUIRED:

Sale Budget Year 5 Quarters
1 2 3 4

Year

Production Budget
Material Budget

Cash Receipts

Cash Payments

In: Accounting

Almost all U.S. light-rail systems use electric cars that run on tracks built at street level....

Almost all U.S. light-rail systems use electric cars that run on tracks built at street level. The Federal Transit Administration claims light-rail is one of the safest modes of travel, with an accident rate of .99 accidents per million passenger miles as compared to 2.29 for buses. The following data show the miles of track and the weekday ridership in thousands of passengers for six light-rail systems.

City Miles of Track Ridership (1000s)
Cleveland 13 16
Denver 15 36
Portland 36 82
Sacramento 19 32
San Diego 45 76
San Jose 29 31
St. Louis 32 43
  1. Use these data to develop an estimated regression equation that could be used to predict the ridership given the miles of track.

    Compute b0 and b1 (to 2 decimals).
    b1  
    b0  

    Complete the estimated regression equation (to 2 decimals).
    y =  +  x
  2. Compute the following (to 1 decimal):
    SSE
    SST
    SSR
    MSE

  3. What is the coefficient of determination (to 3 decimals)? Note: report r2 between 0 and 1.


    Does the estimated regression equation provide a good fit?
    SelectYes, it even provides an excellent fitYes, it provides a good fitNo, it does not provide a good fitItem 10
  4. Develop a 95% confidence interval for the mean weekday ridership for all light-rail systems with 30 miles of track (to 1 decimal).
    (  ,  )
  5. Suppose that Charlotte is considering construction of a light-rail system with 30 miles of track. Develop a 95% prediction interval for the weekday ridership for the Charlotte system (to 1 decimal).
    (  ,  )

    Do you think that the prediction interval you developed would be of value to Charlotte planners in anticipating the number of weekday riders for their new light-rail system?

In: Statistics and Probability