Provide solutions to the following questions

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.A restaurant faces very high demand for its signature mousse desserts in the evening but is less busy during the day. Its manager estimates that inverse demand functions are pe = 30 - Qe in the evening and pd = 16 -Qd during the day, where e and d denote evening and daytime. The marginal cost of producing its dessert evening, MCe, is $8. The marginal cost of producing its dessert daytime, MCd, is $4. There is no fixed cost of producing dessert. Create a spreadsheet with the column headings Qe, Pe, TRe, MRe, TCe, MCe, ne, Qd, Pd, TRd, MRd, TCd, MCd, and nd. (note: ne is profit evening and nd indicates profit daytime) a. What are the optimal prices for the dessert that the restaurant should charge during the evening hours? b. What is the optimal quantity for the dessert that the restaurant should produce during the evening hours? c. What is the total cost of producing the optimal quantity for the dessert during the evening hours? d. What is the maximum profit for the dessert that the restaurant should produce during the evening hours? e. What are the optimal prices for the dessert that the restaurant should charge during the daytime hours? f. What is the optimal quantity for the dessert that the restaurant should produce during the daytime hours? I g. What is the total cost of producing the optimal quantity for the dessert during the daytime hours? h. What is the maximum profit for the dessert that the restaurant should produce during the daytime hours?rnr r'- r" 1.The concept of GDP is used by policy makers for many purposes that include keeping track ofthe growth of our economy and forecasting a recession; but it is also abused by some. Discuss some of the applications of GDP which may be considered improper use or abuse of the concept. 2." Even though the Great Recession ofcially ended, the unemployment rate is still considered high.' Discuss. 3.Discuss how the distribution of income among various groups of income earners have changed in this country during the past 5D years. in your opinion, do we need to initiate any policy to address the distribution of income? Make sure you provide references to anyconclusions you arrive at. 4.Many people feet the Fed, which is largely independent of Congress and the President, is too powerful. In fact, the Chairman of the Fed Board of Governors, Ben Bernanke, has been called the second most powerful person in the country. Do you think the Fed is too powerful? Should Congress have more oversight of the Fed? Share your thoughts. 5."N either monetary policy nor fiscal policy alone can be effective in formulating sound economic policies for recession.' Do you agree or disagree? Share your thoughts. Effou now should realize how important it is for economists to try and predict future conditions of the LLB. economy. Economists are also interested in the performance of the economy at a more local level. Discuss how local and national forecasts play an important role in the State and Federal levels. If here have been significant discussions on the government's scal policy during the Great Recession. in particular, many did not like the government's actions in salvaging the auto industry in providing guaranteed loans to GM and Chrysler. What is your opinion? Provide economic reasons for your opinion