Using Rstudio

# 1. Monty-Hall Three doors

Recall the Monty-Hall game with three doors, discussed in class. Run a simulation to check that the probablility of winning increases to 2/3 if we switch doors at step two.

Set up the experiment two functions "monty_3doors_noswitch" and "monty_3doors_switch" (these functions will have no input values):

```{r}
monty_3doors_noswitch <- function(){
  
}

monty_3doors_switch <- function(){
  
}

```

Use your two functions and the replicate function to compute the empirical probablility of winning for the two experiments.
Compare your answers with the actual theoretical predictions.

```{r}

```

Suppose you work for a small company that produces and sells gourmet pierogi-flavored cookies (yum?) called Babushkies in Northwest Indiana. Your boss has never really paid any attention to the demand for your product before, and one day she asks you to conduct a quantitative demand analysis for Babushkies. She provides you with yearly data from 2000 and 2019 on factors that may be important in the demand for Babushkies, including the price (Px ) and number of Babushkies sold (Qx) , the price of a related good (Py) and the average annual income for Northwest Indiana (M ).

The following steps walk you through the process of conducting a quantitative demand analysis:

1. Estimate a demand function using a regression. Download the provided Problem Set 3 data file (PS3-Data.csv) and use it to estimate the following linear demand function using the regression tool (under Data Analysis) in Excel:

Qxd=α0+αXPx+αyPy+αMM

What is the estimated demand function (you can round estimated coefficients to two significant decimals)? Write this out clearly. Include a copy of your regression output from Excel.

There is some evidence that, in the years 1981 - 85, a simple name change resulted in a short-term increase in the price of certain business firms' stocks (relative to the prices of similar stocks). (See D. Horsky and P. Swyngedouw, "Does it pay to change your company's name? A stock market perspective," Marketing Science v.6, pp. 320- 35, 1987.)

Suppose that, to test the profitability of name changes in the more recent market (the past five years), we analyze the stock prices of a large sample of corporations shortly after they changed names, and we find that the mean relative increase in stock price was about 0.72%, with a standard deviation of 0.14%. Suppose that this mean and standard deviation apply to the population of all companies that changed names during the past five years. Complete the following statements about the distribution of relative increases in stock price for all companies that changed names during the past five years.

(a) According to Chebyshev's theorem, at least____ of the relative increases in stock price lie between 0.51 % and 0.93 %.

(b) According to Chebyshev's theorem, at least ____ of the relative increases in stock price lie between 0.44 % and 1.00 %.

(c) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately____ of the relative increases in stock price lie between 0.44 % and 1.00 %.

(d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 99.7% of the relative increases in stock price lie between___%
and ____%.

There is some evidence that, in the years 1981-85, a simple name change resulted in a short-term increase in the price of certain business firms' stocks (relative to the prices of similar stocks). (See D. Horsky and P. Swyngedouw, "Does it pay to change your company's name? A stock market perspective," Marketing Science v.6 , pp. 320-35,1987.) Suppose that, to test the profitability of name changes in the more recent market (the past five years), we analyze the stock prices of a large sample of corporations shortly after they changed names, and we find that the mean relative increase in stock price was about 0.70%, with a standard deviation of 0.15%. Suppose that this mean and standard deviation apply to the population of all companies that changed names during the past five years. Complete the following statements about the distribution of relative increases in stock price for all companies that changed names during the past five years.

a) According to Chebyshev's theorem, at least of the relative increases in stock price lie between 0.25 % and 1.15.

(b) According to Chebyshev's theorem, at least of the relative increases in stock price lie between 0.40 % and 1.00.

(c) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately of the relative increases in stock price lie between 0.40 % and 1.00.

(d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 68% of the relative increases in stock price lie between _% and _%. .

Suppose the systolic blood pressure (in mm) of adult males has an approximately normal distribution with mean μμ =125 and standard deviation σσ =14.

Create an empirical rule graph with the following:

• A title and label for the horizontal axis including units.
• Vertical lines for the mean and first 3 standard deviations in each direction with numerical labels on the horizontal axis
• Labels for the areas of the 8 regions separated by the vertical lines as well.

Note: This may be hand drawn or computer generated. See the models for desired formats.

a. Upload your completed file below. Choose FileScan Mar 5, 2020 (1).pdf

Now use your graph to answer the following questions.

b. About 95% of men will have blood pressure between what amounts?

and

c. What percentage of men will have a systolic blood pressure outside the range 97 mm to 167 mm?

d. Suppose you are a health practitioner and an adult male patient has systolic blood pressure of 172 mm. Use statistics to explain the gravity of his situation. Structure your essay as follows:

1. A brief description of the normal distribution.
2. Why the normal distribution might apply to this situation.
3. Describe the specific normal distribution for this situation (give the mean and standard deviation)
4. A brief description of the empirical rule
5. What region of the graph (drawn in part a) the individual falls in
6. An estimate of individual's percentile.
7. Why this signifies a health concern.
8. A suggested course of action.

There is some evidence that, in the years 1981-85, a simple name change resulted in a short-term increase in the price of certain business firms' stocks (relative to the prices of similar stocks). (See D. Horsky and P. Swyngedouw, "Does it pay to change your company's name? A stock market perspective," Marketing Science v.6, pp. 320-35,1987.) Suppose that, to test the profitability of name changes in the more recent market (the past five years), we analyze the stock prices of a large sample of corporations shortly after they changed names, and we find that the mean relative increase in stock price was about 0.89%, with a standard deviation of 0.16%. Suppose that this mean and standard deviation apply to the population of all companies that changed names during the past five years. Complete the following statements about the distribution of relative increases in stock price for all companies that changed names during the past five years.

(a) According to Chebyshev's theorem, at least of the relative increases in stock price lie between 0.57 % and 1.21 %.

(b) According to Chebyshev's theorem, at least of the relative increases in stock price lie between 0.65 % and 1.13 %.

(c) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately of the relative increases in stock price lie between 0.57 % and 1.21 %. (d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 99.7% of the relative increases in stock price lie between % and %.

Daddy Warbucks is in the process of adopting Annie from a New York orphanage. He pays $7,000 in 2017, and $7,500 in 2018. Daddy Warbucks’ AGI for 2018 is $165,000. ​

a. How much is the adoption credit that Daddy Warbucks may claim for 2018 if the adoption becomes final in 2018?

b. How much is the adoption credit that Daddy Warbucks may claim for 2018 if the adoption becomes final in 2019?

c. How much is the adoption credit that Daddy Warbucks may claim for 2018 if the adoption falls through and is never finalized?

The following inventory transactions took place near December 31, 2018, the end of the Rasul Company's fiscal year-end:

1. On December 27, 2018, merchandise costing $2,000 was shipped to the Myers Company on consignment. The shipment arrived at Myers's location on December 29, but none of the merchandise was sold by the end of the year. The merchandise was not included in the 2018 ending inventory.
   
2. On January 5, 2019, merchandise costing $8,000 was received from a supplier and recorded as a purchase on that date and not included in the 2018 ending inventory. The invoice revealed that the shipment was made f.o.b. shipping point on December 28, 2018.
   
3. On December 29, 2018, the company shipped merchandise costing $12,000 to a customer f.o.b. destination. The goods, which arrived at the customer's location on January 4, 2019, were not included in Rasul's 2018 ending inventory. The sale was recorded in 2018.
   
4. Merchandise costing $4,000 was received on December 28, 2018, on consignment from the Aborn Company. Purchase was not recorded and the merchandise was not included in the 2018 ending inventory.
   
5. Merchandise costing $6,000 was received and recorded as a purchase on January 8, 2019. The invoice revealed that the merchandise was shipped from the supplier on December 28, 2018, f.o.b. destination. The merchandise was not included in the 2018 ending inventory.

Assignment:

1. State whether Rasul correctly accounted for each of the above transactions. Give the reason for your answer.
   
2. P 8–2 Items to be included in the inventory.

Form a portfolio investing 50% of your money into Amazon and 50% into Pfizer.

a)Calculate the monthly return for each month of the portfolio. Then, provide arithmetic average and standard deviation of the portfolio return. Check and report whether the linear combination (weighted average) of standard deviation of two companies is smaller than portfolio’s standard deviation or not.

b)Calculate the monthly market return, average market return, and market variance using S&P500 Index. Using the variance of market return and covariance between market return and Amazon’s return, calculate the Amazon’s beta. Use =VAR.S() for variance and =COVARIANCE.S() function to get covariance

c)Suppose risk free rate is 1% and expected market return is 5%. Compute the expected return of Amazon using CAPM. You would get the beta in (b)

journalize each transaction.

Background:

Top Quality Appliance - Long Beach has just purchased a franchise from Top Quality Appliance (TQA). TQA is a manufacturer of kitchen appliances. TQA markets its products via retail stores that are operated as franchises. As a TQA franchise, Top Quality Appliance - Long Beach will receive many benefits, including having the exclusive rights to sell TQA brand appliances in Long Beach. In exchange for these benefits, Top Quality Appliance - Long Beach will pay an annual franchise fee to TQA based on a percentage of sales. The annual franchise fee is a separate cost and in addition to the purchase of the franchise. Top Quality Appliances - Long Beach entered into all transactions listed in the Transactions section below during 2018, its first year of operations.

01/01/2018

Received $500,000 cash and issued common stock. Opened a new checking account at Long Beach National Bank and deposited the cash received from the stockholders.

01/01/2018

Paid $50,000 cash for the TQA franchise.

01/01/2018

Paid $75,000 for store fixtures.

01/01/2018

Paid $45,000 for office equipment.

01/01/2018

Paid $600 for office supplies.

01/01/2018

Paid $3,600 for a two-year insurance policy.

01/01/2018

Paid $200,000 cash and issued a $400,000, 10-year, 5% notes payable for land with an existing building. An independent appraiser valued the land and building at $100,000 and $500,000, respectively.

01/10/2018

Purchased appliances from TQA (merchandise inventory) on account for $425,000.

01/15/2018

Established a petty cash fund for $150.

01/20/2018

Sold appliances on account to B&B Contractors for $215,000, terms n/30 (cost, $86,000). Record two separate entries.

02/01/2018

Sold appliances to Davis Contracting for $150,000 (cost, $65,000), receiving a 6-month, 8% note. Record two separate entries.

02/05/2018

Recorded credit card sales of $80,000 (cost, $35,000), net of processor fee of 2%. Record two separate entries.

02/24/2018

Received payment in full from B&B Contractors.

03/01/2018

Purchased appliances from TQA on account, $650,000.

04/01/2018

Made payment on account to TQA, $300,000.

06/01/2018

Sold appliances for cash to LB Home Builders for $350,000 (cost, $175,000). Record two separate entries.

08/01/2018

Received payment in full on the maturity date from Davis Contracting for the note from February 1.

11/01/2018

Sold appliances to Leard Contracting for $265,000 (cost, $130,000), receiving a 9-month, 8% note. Record two separate entries.

11/03/2018

Made payment on account to TQA, $500,000.

11/10/2018

Sold appliances on account to various businesses for $985,000, terms n/30 (cost, $395,000). Record two separate entries.

11/15/2018

Collected $715,000 cash on account.

12/01/2018

Paid cash for expenses: Salaries, $180,000; Utilities, $12,650 (prepare one compound entry).

12/01/2018

Replenished the petty cash fund when the fund had $62 in cash and petty cash tickets for $85 for office supplies.

12/15/2018

Paid dividends, $5,000.

12/31/2018

Paid the franchise fee to TQA of 5% of total sales of $2,045,000.

12/31/2018

The bank reconciliation revealed $1,565 of interest earned on the checking account.

12/31/2018

The bank reconciliation revealed bank fees totaling $2,465 for the year.

12/31/2018

(Adjustment 9) Calculate the interest owed on the note payable.

12/31/2018

(Adjustment 2) Management estimated that 5% of Accounts Receivable will be uncollectible.

12/31/2018

(Adjustment 3) An inventory of office supplies indicates $475 of supplies have been used.

12/31/2018

(Adjustment 4) Accrued interest revenue on the Leard Contracting note (round your answer to the nearest whole dollar).

12/31/2018

(Adjustment 5) Record depreciation expense on the building. The company uses the straight-line depreciation method, and believes the building will last for 30 years and have a $50,000 residual value.

12/31/2018

(Adjustment 6) Record depreciation expense on the fixtures. The company uses straight-line depreciation method, and believes the fixtures will last for 15 years with zero residual value.

12/31/2018

(Adjustment 7) Record depreciation expense on the office equipment. The company uses the double declining-balance depreciation method, and believes the equipment will last for 5 years and have a $5,000 residual value.

12/31/2018

(Adjustment 8) Record amortization expense for the year on the franchise, which has a 10-year life.

12/31/2018

(Adjustment 1) One year of the prepaid insurance has expired.