Tag: Mathematics

Hi Bianca,

You helped me the other day on homework. I was wondering if you are interested in another homework problem to do? This is the following problem……..

Submission instructions: compute and handwrite solutions submit all work/setup which calculations

1a-c. Suppose we have a new type of MBS to accommodate the short-term investor. This new MBS security instrument contains only 5-year mortgages (in reality are rare if non-existent). ACME, a private secondary mortgage market, has pooled together ten $100,000 5-year mortgage loans. Note: To save space in writing out your work, you can scale the ten $100,000 to $100.

Calculate the duration for this MBS pool assuming annual compounding for three years at 10 percent interest which

a.is a “zero coupon”

b. is an interest-only MBS.

c. is fully amortizable over the five years.

2. Now assume that the interest-only MBS in problem 2b. is prepayable (but not defaultable). Use the option-theoretic model to price this MBS. Interest rates have a 50% chance of going up 1% each year and a 50% chance of going down 1% each year. From your results, qualitatively compare the MBS value without prepayment to the MBS value with prepayment. Note: To save space in writing out your work, you can scale the ten $100,000 to $100. – in your solution show the work/setup which includes the calculations for all steps in Slide 17’s Option Pricing Lecture

Only bid if you can guarentee correct answers please. I need the work to be right. Thank you.

Submission instructions: compute and handwrite solutions submit all work/setup which calculations

1a-c.
Suppose we have a new type of MBS to accommodate the short-term
investor. This new MBS security instrument contains only 5-year
mortgages (in reality are rare if non-existent). ACME, a private
secondary mortgage market, has pooled together ten $100,000 5-year
mortgage loans. Note: To save space in writing out your work, you can scale the ten $100,000 to $100.

Calculate the duration for this MBS pool assuming annual compounding for three years at 10 percent interest which

a.is a “zero coupon”

b. is an interest-only MBS.

c. is fully amortizable over the five years.

Now assume that the interest-only MBS in problem 2b. is prepayable (butnot defaultable). Use the option-theoretic model to price this MBS.

Interest rates have a 50% chance of going up 1% each year and a 50%

chance of going down 1% each year. From your results, qualitatively

compare the MBS value without prepayment to the MBS value with

prepayment. Note: To save space in writing out your work, you can scale the ten $100,000 to $100. – in your solution show the work/setup which includes the calculations for all steps in Slide 17’s Option Pricing

• Use this google sheet of responses 
• https://docs.google.com/spreadsheets/d/19i_nMTOlde… these two applets: Reese’s Pieces Simulation http://www.rossmanchance.com/applets/2021/oneprop/…and Normal Probability calculator http://www.rossmanchance.com/applets/2021/normcalc…to complete the PAT.

I’m working on a applied mathematics question and need an explanation to help me learn.

please explain and show proof of the last property for the Bessel functions that is highlighted in the attached screenshot. Only the last property.

Hi tutor, i need your help with these questions, the true/false questions require a short explain for each. Just do your best to explain those, and try to avoid using too many fancy math symbols. Just simple as possible. Good luck.

There are five parts to this discussion: Read, identify three different variable pairs, create table, create graph, describe in words.

Prepare: Prior to beginning work on this discussion, read Chapter 9: Modeling Our World and Chapter 10: Modeling with Geometry in your course text, especially pages 532-3 & 536-9.

For this discussion, identify three different variable pairs in which two quantities appear to be related from either recent news stories, the web, or that you encounter in your everyday life. Each variable pair should come from a different source (as illustrated in the week 4 Discussion Sample) and there should be three sets of paired variables total.

Important note: Only one of the variables can use “time” as an independent variable. For example, you cannot have your variable pairs be (time, dependent variable 1), (time, dependent variable 2) and (time, dependent variable 3). However, you can have your variable pairs be (time, dependent variable 1), (independent variable 2, dependent variable 2) and (independent variable 3, dependent variable 3).

For inspiration, use the examples listed in the solution to Example 1 on p. 537 of the text, or the Week 4 Discussion Sample download, MAT205.W4.DiscussionSample.pdf. Be sure to select different examples!

Create Table

After you have identified three different variable pairs (from distinct sources), make a table of between 10 and 20 entries of data values for each of your variable pairs.

Create Graph

Then, graph your data values for each variable pair and describe in words the function that relates the variables. For each pair, write down at least five (5) points on the graph. Draw the graph using paper & pencil or use an online graphing calculator like Desmos Graphing Calculator (Links to an external site.).

Describe Your Results in Words

For each of the pairs you listed, identify the dependent and independent variables and briefly describe the relationship.

See the week 4 Discussion Sample to see how these go (You must use different examples; you should complete three examples total).

• Your initial post should be at least 250 words in length. It should show all the required math work and explain all the steps. Also include a simple reference for any scholarly resource you used. For example: Washington Post dated August 13, 2018 or retrieved from <url-address> or I consulted example 1 on p. 537 of the text.
• Your initial discussion thread is due on Day 4 (Friday), and you have until Day 7 (Monday) to respond to your classmates. Your grade will reflect both the quality of your initial post and the depth of your responses. Carefully review the Grading Rubric for guidance on how your discussion will be evaluated.

The Easy Way to Plot and Graph Points

Use the Desmos Graphing Calculator (Links to an external site.): (You need not create an account.)

Click on the “+” at the top left corner.

Select “table” from the drop-down menu.

Type in your points. If your point is (2, 30), then x1 is 2 and y1 is 30.

** If your points contain any values beyond  ±10, click the minus sign in the upper right-hand corner a few times to zoom out so you can see the points. **

To add a line connecting the points: 

Click and hold on the circle with four dots on it (next to y1). Click the circle next to “Lines” to show the connecting line. Your graph is done.   

To share the graph, take a screenshot. [This site will show you how: http://www.take-a-screenshot.org/ (Links to an external site.). Click on the tab for Mac or Windows at the top, if needed.] Alternatively, click on the arrow in a box at the upper right hand corner of the screen, then you can “Export Image” as a .png file (it appears in your “Downloads” folder) and attach this to your discussion post or drop and drag into a Word file.

Guided Response: Respond to at least three different peers by Day 7. Give specific thoughtful and substantive responses addressing their points and back up your ideas with references. If you notice classmates forgetting to complete part(s) of the discussion, tactfully encourage them to complete the remaining part(s). Be specific. Give a hint, if possible.

• Have they answered all the questions pertaining to their problem?
• Have they used all the required resources and cited the references correctly?
• Do you understand their answers and agree with their conclusions and viewpoints?
• What are your arguments against their answers?

Student Name: ________________________________

Instructions:

Please answer each of the following questions and show work/calculations. Open up sufficient space in the Word document. Insert your answer using a highlight color (blue, green, red).

Please show your calculations and copy and paste outputs from SPSS and/or Excel into this document.

Please note to consult a Chi=Square (X²) Distribution Table use Appendix B in electronic textbook (p 308) or Google a table.

Good luck.

Question 1: Key Definitions and Concepts Part I (10 points)

1. Explain and define the differences between independent and dependent variables. Give examples. (2 points)
2. Explain and define the differences between the statistical relationships “association” [correlation] and “causation” [causality]. Give examples. (2 points)
3. Explain the difference between an experimental research design and a quasi -experimental research design. Which is the good standard? (2 points)
4. What is sampling error? (2 points)
5. What is the Central Limit Theorem and with is its significance in the field of statistics (2 points)?

Question 2: True False (10 points)

1. Are mean, median, mode, and frequency distribution (or count) statistics of central tendency? True___ False_____ (2 points)
2. Are variance, standard deviation, and statistics of dispersion? True___ False___ (2 points)
3. Will the sampling distribution of an infinite number of relatively large samples be normally distributed? True____ False____ (2 points)
4. Pearson’s Correlation Coefficient is the same at the Spearman Correlation Coefficient
5. Ethics in statistics is not as important as ethics in law and medicine. The latter areas deal with people and the former just with number. True_____ False _____ (2 Points)

True____ False______ (2 points)

Question 3: Key Definitions and Concepts Part II (10 points).

1. Explain the Kolmogorov-Smirnov test, what does it test for, how do you interpret the computer output?
2. What is R-Square?
3. What are the assumptions that must hold for a t-test?
4. What are the assumptions that must hold for ANOVA?
5. What are the Chi-square assumptions?
6. How do you interpret the F Statistic in ANOVA analysis? If the F statistic is significant what does it mean? What does the F Statistic in regression analysis mean?
7. With what types of variables are t-tests used for and with what type of variables are Chi-Square tests used?
8. What are the five steps of hypothesis testing?
9. When do you use the student t distribution?
10. What is the difference between the observed and predicted values of the dependent variable? What is the key assumption made about the error term in regression?

Question 4: Chi-Square (10 points)

Assume that a citizen survey yielding 1,034 responses has been completed. We as statistical analysts what to check for over sampling or under-sampling with respect to US Census data. We want to whether the age distribution of the survey respondents is consistent with the age distribution in the decennial US Census at the 5 percent level of significance.

H_o The age distribution of the sample is consistent or the same as that of the population

H_A The age distribution of the sample is inconsistent or different as that of the population.

Table US Census Response by Age Groups

Age Groups	US Census (Percent)	Survey Sample (Percent)
18-45	62. 3	62.8
46-65	24.1	26.8
66+	13.6	10.4

Write formula, show calculations, determine Chi-Square test value, identify degree of freedom, identify critical value, and make conclusion.

Question 5: Confidence Interval (10 points)

In a sample of 1,000 persons, 15.4 percent of the respondents report personal income at or below the poverty line, whereas 84.6 percent of the respondents report personal income above the poverty line. Please calculate a confidence interval at the 95% and 99% for this proportion of people who live in poverty. Write the appropriate formula to use, apply the formula for proportions, calculate the upper and lower bounds. Show step by step calculations.

1. 95% confidence interval
2. 99% confidence interval

Question 6: One Sample T-Test (10 points)

A psychosocial functional score (PFS) is used to assess school age children’s psychosocial behaviors. A score of 25 points or above is considered normal. A sample of 15 students is tested and their and their PFS corers are as follows:

Case ID	Psychosocial Functional Score (PFS)
1	29
2	32
3	18
4	23
5	27
6	19
7	34
8	32
9	27
10	23
11	26
12	32
13	29
14
15

1. Input the data into SPSS (create new dataset, label Variable PFS_Score).
2. Evaluate whether the students’ average PFS score is greater than 25 using one sample t test. Write a brief explanation of the results of your t test for a non- technical program manager.

What is mean___

What is standard deviation___

What is the t statistic, the 2 tailed significance value, it is less than .05, the mean difference?

Clip and paste SPSS output

Question 7: Paired T-Test (10 points)

Students at a school are given a test before beginning a special program of instruction and then a test after. Used paired samples t-test to determine if there was evidence of improvement (95% level of confidence).

Student	Before Test Score	After Test Score
1	4.5	6.9
2	3.2	4.8
3	5.8	5.2
4	3.9	4.3
5	4.2	5.0
6	3.9	4.8
7	2.6	3.2
8	5.2	4.8
9	4.5	4.5
10	3.9	4.1
11	3.8	3.6
12	4.2	5.9

Clip and paste SPSS output

Report was is the mean difference and confidence interval (95%)

What is test statistic ____

What is p value ____

How does the p value compare to .05 level of significance?

Question 8: Descriptive Statistics and Graphical Exercise (10 points)

1. For the graduation data presented in the table below please calculate mean, variance, and standard deviation for each of the schools (3 points)
2. Produce a line chart for graduation rates for each school. Label graph with title, axis, and legend. (3 points)
3. What is your interpretation of this data and chart? If you were the School Superintendent for the district that includes these two school what sorts of questions would this chart trigger in your mind? What additional investigation would you like to undertake? (4 points)

Graduation Rates (Number of Graduates per Teacher) at Two Different Schools
Year	School A	School B
1	19	33
2	43	25
3	26	32
4	47	32
5	19	32
Mean
Variance
Standard Deviation

Question 9: Simple Linear Regression —Use Excel

[Data–Data Analysis-Select Regression from Dialogue box—filling in boxes with appropriate cell ranges]

1. Please enter the following data into an Excel spreadsheet. Note make sure that you have Data Analysis Tool Pak Installed (Tools -Insert-Excel Add-ins-(click to select Data Analysis Tool Pak) for Microsoft 365 Subscription versions. If you have older versions of Excel see page 108 of Chapter 19 Excel User’s Guide, Section Loading the Data Analysis Tool Pak if not try Help-how to install Add-ins)
2. Run a simple linear regression with DV= EnvironSpend and IV= PopDensity
3. Interpret results.

Data: Environmental Spending

City ID	EnvironSpend	PopDensity
1	0.11	149
2	0.04	44
3	0.26	459
4	0.07	97
5	0.17	345
6	0.13	523
7	0.08	24
8	0.22	275
9	0.11	183
10	0.1	287
11	0.2	137
12	0.11	86
13	0.18	300
14	0.2	260
15	0.15	380

Variable definitions:

City ID==identification code for city

EnivronSpend=Environmental Spending=percent of annual total spending on environmental protection/concerns

PopDensity=population density=number of people per square mile)

Paste output here:

R-Square____ Interpretation______________

Which coefficients are statistically significant and different from zero at the 5% level

Intercept___________________________

Coefficient for PopDensity______________________

What report would you give a non-technical policy maker about the relationship your discovered with your regression analysis? What is the sign of the relationship between population density and environmental spending as a share of total spending? If population density were to increase in a particular jurisdiction what would you tell policy makers to prepare for in preparing future budgets?

Question 10: Multiple Linear Regression-Use SPSS (10 pairs)

Use the SPSS Public Perceptions formatted database (.sav)

1. Run a Linear Regression with an intercept
2. Interpret the sign and meaning of each of the coefficients significantly different from zero. What “economic theory or narrative” could you develop based on the regression findings to explain why people live for long periods in Orange County (Hint: Explain the possible contribution of each significant coefficient/variable)?

Dependent Variable: Yearsorc (Years Lived in Orange County

Independent Variable:

About what is your household income?

Age

Race/ethnicity

Gender

Zipcode of residence

Do you rent or own

How much formal education do you have.

Do you think property taxes are too….

Report R-square and Coefficients for each of the independent variables and significance level

(Clip and Paste SPSS output).

1. The data given below are the temperature readings reported in degree Celsius.15, 23, -18, 19, 26, -5, 12, 27, 19

(a) Which of the following data type categorizations would best describe thetemperature records?A. Categorical/NominalB. OrdinalC. BinaryD. ContinuousE. Discrete

(b) Calculate the range of the temperature records.

(c) Calculate the mode of the temperature records.

Question:

We have discussed the alignment of an organization’s IT architecture with its operations and strategy.  This week, we have a related case from Vermont Teddy Bear.

Please read the attached case study.

Then, in a single post to the Vermont Teddy Bear forum answer the following questions:

1.  How well does Vermont Teddy Bear’s information architecture align with its operations and strategic direction?

2.  What recommendations would you make to increase the effectiveness of the IT organization and architecture in meeting Vermont Teddy Bear’s objectives?