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.In 2008, the policymakers of the economy of Eastlandia projected the debt-GDP ratio and the ratio of the budget deficit to GDP for different scenarios for growth of the deficit over the next 10 years. Real GDP is currently $1,000 Billion per year and is expected to grow by 3% per year; the public debt is $300 billion at the beginning of the year, and the deficit is $30 billion in 2008 Year Real GDP Debt Budget Deficit Debt Budget Deficit Billions of $) Billions of $) % of GDP) (X GDP) 2008 1,000 300 30 200 1,030 30 2010 1,061 30 2011 1,093 DE 2012 1,126 30 2013 1,159 30 2014 1,194 30 2015 1,230 30 2016 1,267 30 2017 1,305 30 2018 1,344 30 ) Complete the table above if the deficit remains constant at $30 for the entire period. Remember that the government's debt will grow by the previous year's deficit. b) Now redo the table given that the deficit now grows by 3% every year during the period. Year Real GDP Deb Budget Deficit Debt Budget Deficit Billions of $) (Billions of $) (% of GDP) %% GDP) 2008 1,000 300 30 1009 1,030 2010 1,061 2011 1,093 2012 1,120 201 1,159 2014 1,194 2015 1,230 2016 1,267 2017 1,30 2018 1,344 c) What happens to the Debt-GDP ratio and the deficit-GDP ratio for the economy over time under the different scenarios? d) Which scenario would be preferable for this country? Why?MeJO A Unit 01 - The Capitalist Revolution Homework Instructions: This homework will provide you with an opportunity to apply the ideas and concepts from the chapter readings, lecture notes, and videos. You should (1) write out the answers to each question either in the space provided in this document, or on separate paper, then for class credit, (2) submit your answers using the appropriate unit homework quiz on D2L/Brightspace. Question 01a: GDP per capita - According to the World Bank, for 2018 Mexico had a Gross Domestic Product or GDP of 1,220,699 million in US dollars. The population of Mexico in 2018 was 126,190,788. Calculate Mexico's GDP per person for 20181. Question 01b: GDP per capita - Based on your calculation, do you think the average Mexican's standard of living is higher, lower, the same, as the average American? Think about if GDP per capita is a good measure of our well-being?+ Quizaquiz probGuid=(NAPCOA$01010001003594-40200400008cix-smedcalle1-00018ck-8_14919842 10 C Q Sand 1. Pricing foreign goods As Aa The exchange rate Is the price of one currency in terms of another currency. An exchange rate specifies how many 1. Pricing foreign goods An Aa The exchange rate Is the price of one currency in terms of another currency. An exchange rate specifies how many units of one country's currency equal one unit of another country's currency. Suppose the following table forecasts exchange rate data for November 26, 2014, in terms of U.S. dollars per unit of foreign currency. Use the information in the table to answer the questions that follow. U.S. Dollars ($) Foreign Currency per Unit of Foreign Currency Brazilian real (R$) 0.3666 Canadian dollar (CDN$) 0.8493 Euro (C ) 1.3288 Japanese yen (#) 0.009748 Mexican peso (MEX$) 0.0889 UK pound (E) 1.8965 Suppose that on November 26, 2014, a children's doll handmade in Japan is priced at V1,000. The approximate U.S. dollar price of the doll would be If the exchange rate for the U.S. dollar-Japanese yen falls from the rate given by the table to $0.0047 per yen, the value of the U.S. dollar relative to the yen. Grade It Now Save & Continue