This is a more general version of Problem C.1. Let Y1, Y2, …, Yn be n pairwise uncorrelated random variables with common mean m and common variance 2. Let Y denote the sample average. (i) Define the class of linear estimators of m by Wa a1Y1 a2Y2 … anYn,
where the ai are constants. What restriction on the ai is needed for Wa to be an unbiased estimator of m?
(ii) Find Var(Wa).
(iii) For any numbers a1, a2, …, an, the following inequality holds: (a1 a2 … an)2/n a1 a2 … an. Use this, along with parts (i) and (ii), to show that
2 2 2
Var(Wa) Var(Y) whenever Wa is unbiased, so that Y is the best linear unbiased estimator. [Hint: What does the inequality become when the ai satisfy the restriction from part (i)]

Amarket that consists of all possible consumers regardless of their specific needs or wants is a

Net income and owner's equity for four businesses four different proprietorships, jupiter, mars, saturn, and venus, show the same balance sheet data at the beginning and end of a year. these data, exclusive of the amount of owner's equity, are summarized as follows: total assets total liabilities beginning of the year $550,000 $215,000 end of the year 844,000 320,000 on the basis of the preceding data and the following additional information for the year, determine the net income (or loss) of each company for the year. (hint: first determine the amount of increase or decrease in owner's equity during the year.) jupiter: the owner had made no additional investments in the business and had made no withdrawals from the business. mars: the owner had made no additional investments in the business but had withdrawn $36,000. saturn: the owner had made an additional investment of $60,000 but had made no withdrawals. venus: the owner had made an additional investment of $60,000 and had withdrawn $36,000. jupiter net income $ mars net income $ saturn net income $ venus net income $

Doogan corporation makes a product with the following standard costs: standard quantity or hours standard price or rate direct materials 2.0 grams $ 7.00 per gram direct labor 1.6 hours $ 12.00 per hour variable overhead 1.6 hours $ 6.00 per hour the company produced 5,000 units in january using 10,340 grams of direct material and 2,320 direct labor-hours. during the month, the company purchased 10,910 grams of the direct material at $7.30 per gram. the actual direct labor rate was $12.85 per hour and the actual variable overhead rate was $5.80 per hour. the company applies variable overhead on the basis of direct labor-hours. the direct materials purchases variance is computed when the materials are purchased. the materials quantity variance for january is: