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QM Course Reflective Write-up
In your reflective writeup, take 3-5 pages to discuss the methods introduced in the class (regression, forecasting, foresi ...
QM Course Reflective Write-up
In your reflective writeup, take 3-5 pages to discuss the methods introduced in the class (regression, forecasting, foresight, and agile strategy). Specifically, what new insights did you gain? Which one(s) will be most useful in your career? What are potential applications for the methods in your current position? Have you begun using any of the methods outside the class?
Math 161A Statistics Probability Writing Project
1. (6 points) How large would a potential Jackpot have to be in the California Mega
Millions Lottery in order for the gam ...
Math 161A Statistics Probability Writing Project
1. (6 points) How large would a potential Jackpot have to be in the California Mega
Millions Lottery in order for the game to be fair? Present your computation and
explain your reasoning in addition to stating your final answer.
Note: A fair game is one in which in the long-run neither party (lottery company
and players) has an advantage.
2. There are a number of probability claims made in the Lottery tips. In this problem,
you will verify whether these claims are true. Consider the current rules (5/70 +
1/25) of the CA MEGA millions game.
(a) (5 points) Consider the Odd-Even Lotto Tip. Find the exact probability that
the five white numbers selected will all be even.
(b) (8 points) Consider the Sum Lotto Tip. Use the Central Limit Theorem to
approximate the probability that the sum of the five white balls will fall between
132 and 223 (both inclusive).
Discuss the appropriateness of using the Central Limit Theorem in this case. If
any of the assumptions of the theorem are violated, state what these assumtions
are and discuss how extreme (mild, moderate, severe) the violation is.
(c) (6 points) Consider the Repeat Hits Lottery Tip. It is not entirely clear, whether
this tip only concerns the white balls or also the gold MEGA ball.
i. Find the exact probability that in a given drawing at least one of the white
numbers is a repeat from the last drawing.
ii. Find the exact probability that in a given drawing at least one of the six
balls drawn (five white and one gold) is a repeat of the last drawing.
(d) (5 points) Consider the Tip that recommends to avoid previous number combinations. How long, on average (in years), will it take until a given set of MEGA
million lottery numbers (five white balls and MEGA ball) will be repeated in
a drawing? Recall, that drawings take place bi-weekly and that assume that a
year has 365 days (i.e., ignore leap years).
3. (5 points) Assume that game payouts are fixed (not pari-mutuel). Will following the
advice of the lottery expert increase your chances of winning the lottery? (This is a
multiple choice question - Yes/No answer ONLY.)
4. (10 points) Discuss the advice from the Lotto-Expert presented on page 2. Are the
statements made in the individual tips presented there generally truthful? Do they
hold for general (future) drawings, and not just for data collected in the past? Is
following this advice a good idea when playing the lottery? Explain why or why not.
Take a stand and defend your position with a good logical argument using the
methods of probability you have learned in this course. Provide as much numerical
evidence as necessary (you may cite your results from problem 2) to support your
3
Math 161A - Fall 2020 M. Bremer
claim(s). Make sure to provide a cohesive argument (using correct spelling and good
grammar).
5. (5 points) To study whether the drawing of lottery numbers for the MEGA million
game is truly random, we will consider some data. The data (which are available
in the file “Lottery Data.csv”) contains the date of the drawing, the five white balls
drawn, and the MEGA ball drawn in all 1925 drawings of the NY MEGA millions
between 5/17/2002 and 11/03/2020.
Based on the graphs that you can find on the next pages, discuss whether it is reasonable to assume that lottery numbers are drawn independently and at random
meaning that each possible number combination is equally likely to be drawn. Describe which aspect(s) of which graph(s) you base your conclusion on.
Disclaimer: The data come from the New York State (not the California State)
MEGA millions lottery. Like California, NY has changed the rules for the MEGA
millions game several times over the last couple years. For instance, on October 19,
2013, they switched from drawing 55 white balls to drawing 75 white balls. On the
same date, the number of possible MEGA balls were reduced from 45 to 15. Another
rule change occurred in October 2017.
Note: You are welcome to look at the raw data and/or create your own additional
graphs if you wish, but that’s not required for this problem.
Grading: Your work will be graded
Statistic Assignment
It is a Statistic Assignment Using Technology to Produce Scatterplots and Regression Equations. All the information is dow ...
Statistic Assignment
It is a Statistic Assignment Using Technology to Produce Scatterplots and Regression Equations. All the information is down bellow in drop file. Thank you
BHS A contractor recorded the amount of money earned for different jobs and the amount of time spent on each job.
A contractor recorded the amount of money earned for different jobs and
the amount of time spent on each job. The data a ...
BHS A contractor recorded the amount of money earned for different jobs and the amount of time spent on each job.
A contractor recorded the amount of money earned for different jobs and
the amount of time spent on each job. The data are shown in the
scatterplot below. Based on the data, predict the amount of money the
carpenter would earn from a job that took 15 days to complete.A. $1500B. $3500C. $1000D. $3000
AUMC Rates of Return Market Index & Average Annual Return in Excel Worksheet
Problem Set #3Attached Files: Question 1 - Building a Model - Goodman & Landry Data.xlsx (18.865 KB)Question 1The attached ...
AUMC Rates of Return Market Index & Average Annual Return in Excel Worksheet
Problem Set #3Attached Files: Question 1 - Building a Model - Goodman & Landry Data.xlsx (18.865 KB)Question 1The attached file contains hypothetical data for working this problem. Goodman Corporation’s and Landry Incorporated’s stock prices and dividends, along with the Market Index, are shown in the file. Stock prices are reported for December 31 of each year, and dividends reflect those paid during the year. The market data are adjusted to include dividends.Use the data given to calculate annual returns for Goodman, Landry, and the Market Index, and then calculate average returns over the five-year period. (Hint: Remember, returns are calculated by subtracting the beginning price from the ending price to get the capital gain or loss, adding the dividend to the capital gain or loss, and dividing the result by the beginning price. Assume that dividends are already included in the index. Also, you cannot calculate the rate of return for 2015 because you do not have 2014 data.)Calculate the standard deviation of the returns for Goodman, Landry, and the Market Index. (Hint: Use the sample standard deviation formula given in the chapter, which corresponds to the STDEV function in Excel.) On a stand-alone basis which corporation is the least risky?Construct a scatter diagram graph that shows Goodman’s and Landry’ returns on the vertical axis and the Market Index’s returns on the horizontal axis. Estimate Goodman’s and Landry’s betas as the slopes of regression lines with stock returns on the vertical axis (y-axis) and market return on the horizontal axis (x-axis). (Hint: use Excel’s SLOPE function.) Are these betas consistent with your graph?The risk-free rate on long-term Treasury bonds is 8.04%. Assume that the market risk premium is 6%. What is the expected return on the market? Now use the SML equation to calculate the two companies' required returns.If you formed a portfolio that consisted of 60% Goodman stock and 40% Landry stock, what would be its beta and its required return?Suppose an investor wants to include Goodman Industries’ stock in his or her portfolio. Stocks A, B, and C are currently in the portfolio, and their betas are 0.769, 0.985, and 1.423, respectively. Calculate the new portfolio’s required return if it consists of 30% of Goodman, 20% of Stock A, 30% of Stock B, and 20% of Stock C.Question 2Quest Financial services balance sheets report $200 million in total debt, $100 million in short-term investments, and $30 million in preferred stock. Quest has 10 million shares of common stock outstanding. A financial analyst estimated that Quest’s value of operations is $1000 million. What is the analyst’s estimate of the intrinsic stock price per share?Question 3Lincoln Incorporated is expected to pay a $4.5 per share dividend at the end of this year (i.e., D1 = $4.50). The dividend is expected to grow at a constant rate of 5% a year. The required rate of return on the stock is, rs, is 12%. What is the estimated value per share of Boehm stock?Question 4Assume that the average firm in Masters Corporation’s industry is expected to grow at a constant rate of 3% and that its dividend yield is 5%. Masters is about as risky as the average firm in the industry and just paid a dividend (D0) of $2.5. Analysts expect that the growth rate of dividends will be 25% during the first year (g0,1 = 25%) and 10% during the second year (g1,2 = 10%). After Year 2, dividend growth will be constant at 5%. What is the required rate of return on Masters’s stock? What is the estimated intrinsic per share?Question 5Several years ago, Macro Riders issued preferred stock with a stated annual dividend of 5% of its $600 par value. Preferred stock of this type currently yields 10%. Assume dividends are paid annually.a. What is the estimated value of Macro’s preferred stock? b. Suppose interest rate levels have risen to the point where the preferred stock now yields 14%. What would be the new estimated value of Macro’s preferred stock?Question 61. Define each of the following terms:Call optionPut optionStrike price or exercise priceExpiration dateExercise valueOption priceTime valueWriting an optionCovered optionNaked optionIn-the-money callOut-of-the-money callLEAPS2. The current price of a stock is $50. In 1 year, the price will be either $65 or $35. The annual risk-free rate is 10%. Find the price of a call option on the stock that has an exercise price of $55 and that expires in 1 year. (Hint: Use daily compounding.)3. The exercise price on one of Chrisardan Company’s call options is $20, its exercise value is $27, and its time value is $8. What are the option’s market value and the price of the stock?Submit your answers in a Word document.
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QM Course Reflective Write-up
In your reflective writeup, take 3-5 pages to discuss the methods introduced in the class (regression, forecasting, foresi ...
QM Course Reflective Write-up
In your reflective writeup, take 3-5 pages to discuss the methods introduced in the class (regression, forecasting, foresight, and agile strategy). Specifically, what new insights did you gain? Which one(s) will be most useful in your career? What are potential applications for the methods in your current position? Have you begun using any of the methods outside the class?
Math 161A Statistics Probability Writing Project
1. (6 points) How large would a potential Jackpot have to be in the California Mega
Millions Lottery in order for the gam ...
Math 161A Statistics Probability Writing Project
1. (6 points) How large would a potential Jackpot have to be in the California Mega
Millions Lottery in order for the game to be fair? Present your computation and
explain your reasoning in addition to stating your final answer.
Note: A fair game is one in which in the long-run neither party (lottery company
and players) has an advantage.
2. There are a number of probability claims made in the Lottery tips. In this problem,
you will verify whether these claims are true. Consider the current rules (5/70 +
1/25) of the CA MEGA millions game.
(a) (5 points) Consider the Odd-Even Lotto Tip. Find the exact probability that
the five white numbers selected will all be even.
(b) (8 points) Consider the Sum Lotto Tip. Use the Central Limit Theorem to
approximate the probability that the sum of the five white balls will fall between
132 and 223 (both inclusive).
Discuss the appropriateness of using the Central Limit Theorem in this case. If
any of the assumptions of the theorem are violated, state what these assumtions
are and discuss how extreme (mild, moderate, severe) the violation is.
(c) (6 points) Consider the Repeat Hits Lottery Tip. It is not entirely clear, whether
this tip only concerns the white balls or also the gold MEGA ball.
i. Find the exact probability that in a given drawing at least one of the white
numbers is a repeat from the last drawing.
ii. Find the exact probability that in a given drawing at least one of the six
balls drawn (five white and one gold) is a repeat of the last drawing.
(d) (5 points) Consider the Tip that recommends to avoid previous number combinations. How long, on average (in years), will it take until a given set of MEGA
million lottery numbers (five white balls and MEGA ball) will be repeated in
a drawing? Recall, that drawings take place bi-weekly and that assume that a
year has 365 days (i.e., ignore leap years).
3. (5 points) Assume that game payouts are fixed (not pari-mutuel). Will following the
advice of the lottery expert increase your chances of winning the lottery? (This is a
multiple choice question - Yes/No answer ONLY.)
4. (10 points) Discuss the advice from the Lotto-Expert presented on page 2. Are the
statements made in the individual tips presented there generally truthful? Do they
hold for general (future) drawings, and not just for data collected in the past? Is
following this advice a good idea when playing the lottery? Explain why or why not.
Take a stand and defend your position with a good logical argument using the
methods of probability you have learned in this course. Provide as much numerical
evidence as necessary (you may cite your results from problem 2) to support your
3
Math 161A - Fall 2020 M. Bremer
claim(s). Make sure to provide a cohesive argument (using correct spelling and good
grammar).
5. (5 points) To study whether the drawing of lottery numbers for the MEGA million
game is truly random, we will consider some data. The data (which are available
in the file “Lottery Data.csv”) contains the date of the drawing, the five white balls
drawn, and the MEGA ball drawn in all 1925 drawings of the NY MEGA millions
between 5/17/2002 and 11/03/2020.
Based on the graphs that you can find on the next pages, discuss whether it is reasonable to assume that lottery numbers are drawn independently and at random
meaning that each possible number combination is equally likely to be drawn. Describe which aspect(s) of which graph(s) you base your conclusion on.
Disclaimer: The data come from the New York State (not the California State)
MEGA millions lottery. Like California, NY has changed the rules for the MEGA
millions game several times over the last couple years. For instance, on October 19,
2013, they switched from drawing 55 white balls to drawing 75 white balls. On the
same date, the number of possible MEGA balls were reduced from 45 to 15. Another
rule change occurred in October 2017.
Note: You are welcome to look at the raw data and/or create your own additional
graphs if you wish, but that’s not required for this problem.
Grading: Your work will be graded
Statistic Assignment
It is a Statistic Assignment Using Technology to Produce Scatterplots and Regression Equations. All the information is dow ...
Statistic Assignment
It is a Statistic Assignment Using Technology to Produce Scatterplots and Regression Equations. All the information is down bellow in drop file. Thank you
BHS A contractor recorded the amount of money earned for different jobs and the amount of time spent on each job.
A contractor recorded the amount of money earned for different jobs and
the amount of time spent on each job. The data a ...
BHS A contractor recorded the amount of money earned for different jobs and the amount of time spent on each job.
A contractor recorded the amount of money earned for different jobs and
the amount of time spent on each job. The data are shown in the
scatterplot below. Based on the data, predict the amount of money the
carpenter would earn from a job that took 15 days to complete.A. $1500B. $3500C. $1000D. $3000
AUMC Rates of Return Market Index & Average Annual Return in Excel Worksheet
Problem Set #3Attached Files: Question 1 - Building a Model - Goodman & Landry Data.xlsx (18.865 KB)Question 1The attached ...
AUMC Rates of Return Market Index & Average Annual Return in Excel Worksheet
Problem Set #3Attached Files: Question 1 - Building a Model - Goodman & Landry Data.xlsx (18.865 KB)Question 1The attached file contains hypothetical data for working this problem. Goodman Corporation’s and Landry Incorporated’s stock prices and dividends, along with the Market Index, are shown in the file. Stock prices are reported for December 31 of each year, and dividends reflect those paid during the year. The market data are adjusted to include dividends.Use the data given to calculate annual returns for Goodman, Landry, and the Market Index, and then calculate average returns over the five-year period. (Hint: Remember, returns are calculated by subtracting the beginning price from the ending price to get the capital gain or loss, adding the dividend to the capital gain or loss, and dividing the result by the beginning price. Assume that dividends are already included in the index. Also, you cannot calculate the rate of return for 2015 because you do not have 2014 data.)Calculate the standard deviation of the returns for Goodman, Landry, and the Market Index. (Hint: Use the sample standard deviation formula given in the chapter, which corresponds to the STDEV function in Excel.) On a stand-alone basis which corporation is the least risky?Construct a scatter diagram graph that shows Goodman’s and Landry’ returns on the vertical axis and the Market Index’s returns on the horizontal axis. Estimate Goodman’s and Landry’s betas as the slopes of regression lines with stock returns on the vertical axis (y-axis) and market return on the horizontal axis (x-axis). (Hint: use Excel’s SLOPE function.) Are these betas consistent with your graph?The risk-free rate on long-term Treasury bonds is 8.04%. Assume that the market risk premium is 6%. What is the expected return on the market? Now use the SML equation to calculate the two companies' required returns.If you formed a portfolio that consisted of 60% Goodman stock and 40% Landry stock, what would be its beta and its required return?Suppose an investor wants to include Goodman Industries’ stock in his or her portfolio. Stocks A, B, and C are currently in the portfolio, and their betas are 0.769, 0.985, and 1.423, respectively. Calculate the new portfolio’s required return if it consists of 30% of Goodman, 20% of Stock A, 30% of Stock B, and 20% of Stock C.Question 2Quest Financial services balance sheets report $200 million in total debt, $100 million in short-term investments, and $30 million in preferred stock. Quest has 10 million shares of common stock outstanding. A financial analyst estimated that Quest’s value of operations is $1000 million. What is the analyst’s estimate of the intrinsic stock price per share?Question 3Lincoln Incorporated is expected to pay a $4.5 per share dividend at the end of this year (i.e., D1 = $4.50). The dividend is expected to grow at a constant rate of 5% a year. The required rate of return on the stock is, rs, is 12%. What is the estimated value per share of Boehm stock?Question 4Assume that the average firm in Masters Corporation’s industry is expected to grow at a constant rate of 3% and that its dividend yield is 5%. Masters is about as risky as the average firm in the industry and just paid a dividend (D0) of $2.5. Analysts expect that the growth rate of dividends will be 25% during the first year (g0,1 = 25%) and 10% during the second year (g1,2 = 10%). After Year 2, dividend growth will be constant at 5%. What is the required rate of return on Masters’s stock? What is the estimated intrinsic per share?Question 5Several years ago, Macro Riders issued preferred stock with a stated annual dividend of 5% of its $600 par value. Preferred stock of this type currently yields 10%. Assume dividends are paid annually.a. What is the estimated value of Macro’s preferred stock? b. Suppose interest rate levels have risen to the point where the preferred stock now yields 14%. What would be the new estimated value of Macro’s preferred stock?Question 61. Define each of the following terms:Call optionPut optionStrike price or exercise priceExpiration dateExercise valueOption priceTime valueWriting an optionCovered optionNaked optionIn-the-money callOut-of-the-money callLEAPS2. The current price of a stock is $50. In 1 year, the price will be either $65 or $35. The annual risk-free rate is 10%. Find the price of a call option on the stock that has an exercise price of $55 and that expires in 1 year. (Hint: Use daily compounding.)3. The exercise price on one of Chrisardan Company’s call options is $20, its exercise value is $27, and its time value is $8. What are the option’s market value and the price of the stock?Submit your answers in a Word document.
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