Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

Question 1 (understanding mean and variance of linear combinations of random variables) Let T_15 be the percentage of adult males who used tobacco products in

image text in transcribedimage text in transcribedimage text in transcribed

image text in transcribedimage text in transcribedimage text in transcribed
Question 1 (understanding mean and variance of linear combinations of random variables) Let T_15 be the percentage of adult males who used tobacco products in 2015 in a country and T_10 be this percentage in 2010 in the same country. Define the random variable Z in the following way: Z =T_15 -T_10. We do not observe T_15 and T_10 for all countries of the world. We can only hope to get data from a random sample of n countries, where n is much smaller than the number of countries in the world. We want to estimate the E (Z) for the distribution of countries in the world. Each group member should attempt one of the following questions. The group can consult and improve the answer and only submit the improved answer, but the original person who attempted each part must be named. 1. What does the hypothesis E (Z) = 0 mean? After explaining what this hypothesis means, describe whether or not E (Z) = 0 implies T_15 = T_10 in every country in the world. Then, describe whether or not E (Z) = 0 implies -Er_15; = -Er_10; 1= 1 1= 1 for the n countries in the sample [Note that "Yes it does" or "No it doesn't" are not sufficient, you are expected to justify your answer.] 2. Using the result that sample average is an unbiased estimator of the population mean, show that iz = MET_15; - MELT_10; is an unbiased estimator of E (Z) . 3. Using the result that the variance of the sample average of a random sample of n observations from a distribution with mean / and variance o' is , compute the variance of /z = > >_,T_15; - " Ein T_10;, for a random sample of n = 40 countries, when Var (T_15) = Var(T_10) = 100, and p the correlation coefficient between 7_15 and T_10 is 0.8. 4. Suppose that we have obtained data on T_15 and T_10 for a sample n countries and computed Z; =T_15; -T_10; for i = 1, ..., n. Using the matrix formula for the OLS estimator, show that if we regress this variable on a constant only, the OLS estimate of the constant will be ! )_, T_15;- = ELIT_10.Question 1 (understanding mean and variance of linear combinations of random variables) Let T_15 be the percentage of adult males who used tobacco products in 2015 in a country and T_10 be this percentage in 2010 in the same country. Define the random variable Z in the following way: Z =T_15 -T_10. We do not observe T_15 and T_10 for all countries of the world. We can only hope to get data from a random sample of n countries, where n is much smaller than the number of countries in the world. We want to estimate the E (Z) for the distribution of countries in the world. Each group member should attempt one of the following questions. The group can consult and improve the answer and only submit the improved answer, but the original person who attempted each part must be named. 1. What does the hypothesis E (Z) = 0 mean? After explaining what this hypothesis means, describe whether or not E (Z) = 0 implies T_15 = T_10 in every country in the world. Then, describe whether or not E (Z) = 0 implies -Er_15; = -Er_10; 1= 1 1= 1 for the n countries in the sample [Note that "Yes it does" or "No it doesn't" are not sufficient, you are expected to justify your answer.] 2. Using the result that sample average is an unbiased estimator of the population mean, show that iz = MET_15; - MELT_10; is an unbiased estimator of E (Z) . 3. Using the result that the variance of the sample average of a random sample of n observations from a distribution with mean / and variance o' is , compute the variance of /z = > >_,T_15; - " Ein T_10;, for a random sample of n = 40 countries, when Var (T_15) = Var(T_10) = 100, and p the correlation coefficient between 7_15 and T_10 is 0.8. 4. Suppose that we have obtained data on T_15 and T_10 for a sample n countries and computed Z; =T_15; -T_10; for i = 1, ..., n. Using the matrix formula for the OLS estimator, show that if we regress this variable on a constant only, the OLS estimate of the constant will be ! )_, T_15;- = ELIT_10.73. Comparing a competitor's product unfavorably to your product establishes liability for tortious interference with prospective advantage. True or False? 74. What is negligence? 75. Describe a fact situation in which a defendant can be charged with negligence per se. 76. In trying out a bat in the gift shop at Coors Field, defendant broke a display case. That scared the shop cat, who knocked over a candle. Is defendant liable for the resulting damage to the gift shop? Why or why not? 77. Warren Buffett offered you a job as a stock analyst for a salary he will decide after he reviews your resume. Do you have an employment contract with Mr. Buffett? Why or why not?_ 78. If you move to Omaha in reasonable reliance on your conversation with Mr. Buffett, what theory could you plead to recover the cost of your move? 79. An offer to pay a $100 reward for the return of my lost cat is an offer to enter into which type of contract? a. A bilateral contract b. An implied contract C. A unilateral contract d. A quasi-contract 80. A contract for the sale of goods that were later destroyed in a hurricane may be defended based on #1. Obligations under a performance contract may be assigned to another party unless [Circle off that apply) 82. The elements needed to prove a prima facie case of employment discrimination are (Circle all that apply) a. Plaintiff is a member of a protected class b. Plaintiff engaged in a protected activity C. Employer took tangible employment action against the plaintiff d. Employer's action was taken because of plaintiff's protected activity83. The elements needed to prove a prima facie case of retaliation for engaging in a protected activity are (Circle all that apply) a. Plaintiff is a member of a protected class b. Plaintiff engaged in a protected activity c. Employer took tangible employment action against the plaintiff d. Employer's action was taken because of plaintiff's protected activity 84. An employee may sue his employer based on an employment relationship under which of the following possible theories? (Circle all that apply) a. An employment handbook created a contract b. The employer's action violated a public policy protecting Colorado employees c. The employee reported the employer's illegal conduct to a law enforcement agency d. The employer invaded the employee's privacy rights 85. Identify a important advantage of incorporation. 86. All partners in a limited liability partnership are liable for the professional malpractice of each partner. True or False? 87. The easiest business entity to form is the 88. A sale of real property includes both the land and 89. A person who finds mislaid property has no rights to keep the property. True or False? 90. A real estate purchaser of land would prefer a warranty deed over a quit claim deed because 91. A landowner has a duty to warn a person who enters his land of known dangers. True or False? 92. In Colorado, a hand-written and signed will is effective, even without witnesses. True or False? 93. Interference with the general public's use or enjoyment of public land is known as the tort of - 94. The four types of intellectual property are patent, trademark and trade name. 95. Patents must be both and non-obvious. 95. An author must register a creative work with the U.S. Copyright Office in order to obtain damages in a suit for copyright 97. A trade secret is protected from misappropriation as long as the formula, device, process or other business Information remains

Step by Step Solution

There are 3 Steps involved in it

Step: 1

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image_2

Step: 3

blur-text-image_3

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

Economics

Authors: Roger A. Arnold

11th edition

1133561675, 978-1133561675

More Books

Students also viewed these Economics questions

Question

List t he t hree c omponents of ident ity. (p. 3 0)

Answered: 1 week ago

Question

Do not get married, wait until I come, etc.

Answered: 1 week ago

Question

Do not come to the conclusion too quickly

Answered: 1 week ago

Question

Engage everyone in the dialogue

Answered: 1 week ago