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)]

Suppose you hold a portfolio consisting of a $10,000 investment in each of 8 different common stocks. the portfolio's beta is 1.25. now suppose you decided to sell one of your stocks that has a beta of 1.00 and to use the proceeds to buy a replacement stock with a beta of 1.55. what would the portfolio's new beta be? do not round your intermediate calculations.

Juan's investment portfolio was valued at $125,640 at the beginning of the year. during the year, juan received $603 in interest income and $298 in dividend income. juan also sold shares of stock and realized $1,459 in capital gains. juan's portfolio is valued at $142,608 at the end of the year. all income and realized gains were reinvested. no funds were contributed or withdrawn during the year. what is the amount of income juan must declare this year for income tax purposes?

Amanufacturing firm is considering overhauling the existing compensation strategy. currently every front line employee who works on the assembly line earns the same hourly wage. ideally, management would like to institute a new pay system that involves pay-for-performance. which of the following recommendations is both consistent with scientific management's general emphases and generally good advice for management of this firma. the firm should adopt a differential pay system with one pay level for average performance, and a higher level for good performance. b. the firm should adopt a differential pay system, but the firm should modify it from its original design and provide many different levels of pay associated with different performance levels. c. the firm should understand worker psychology and to focus on pay as the key motivator. d. all of the abovee. none of the above