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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.ocew/content/group/1:406fble 2593-423d-bf71-710356373a56/Problem?120sets/Lcon101P57.pdf of quantity. Then find marginal revenue as the derivative of total revenue with respect to quantity. Plot MR, and explain why it is downward sloping- (e) The monopolist's optimal quantity occurs where MC crosses MR. Mark this quantity on the graph, and make sure it matches your answer to 2(d)- (f) Also mark the monopolist's price Pm from 2(e). Is this price above or bekes ATC at that quantity? Explain why you knew that would be the case. (g) The competitive market outcome happens when the demand function crosses marginal cost (the supply function in a competitive market). Find p" and y" as if the market were competitive. Mark these on the graph. 4. This question concerns surplus and efficiency of the market under monopoly. (a) On the graph you just drew, shade/color (and label) the areas corresponding to producer and consumer surplus under the monopoly outcome. (b) Calculate consumer and producer surplus. Note that producer surplus is a trapezoid; you can calculate its area either by splitting it into a rectangle and a triangle, or by using the formula for the area of a trapezoid (Google it if you don't know). (e) Recall that producer surplus is profit plus fixed cost. Is that the case here? (d) On the graph you drew in question 2, shade/color (and label) the area that represents the deadweight loss from having the monopolist outcome (Pa. ym) rather than the com- petitive outcome (p' y') then calculate its value. 8A DOC.DdE AaBb CcDdl A BbCDdBe ABC DIF: ABC:UdBe Body Tail Heading Heading 2 List Paragraph No Spacing Normal Question 5 (14 marks) On 1 July 2017, Montana Ltd had an opening balance for accounts receivable of $90,000 DR and an allowance for doubtful debt of $25,000 CR. On 3 October 2017, Montana made $60,000 of credit sales to customers. On 5 December 2017, a customer BHP declared bankruptcy and would not be able to pay the amount of 10,000 owed. On 3 April, 2018, BHP managed to repay 20 cents in the dollar. Montana used the percentage of credit sales method to estimate doubtful debt expense at year end of 2018. Past experience suggests that 2% of credit sales are uncollectible. Starting from 1 July 2018, Montana switched to a percentage of accounts receivable method to estimate bad debt. At 30 June 2019, Montana had accounts receivable of $1,000,000 and doubtful debts were estimated based on 3% of accounts receivable. Since 1 July 2019, Montana started to use an aging analysis of accounts receivable to estimate bad debt. Below is an account receivable aging chart by 30 June 2020. Customer name 0-30 Days 31-60 Days 61-90 Days 90+ Days Holden $40,000 $40,000 Canva $10,000 $90,000 $70,000 CBH Group $40,000 Percentage 1% 3% 10% 20%