= 2 = 45 3. The total profit for N = 5 of the largest computer...

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= 2 = 45 3. The total profit for N = 5 of the largest computer companies was known to be Y = 500 (million dollars). For a sample of n 9 from the remaining N computer companies, the sample mean and the standard deviation were = 30 and S = 15. An estimate suggested for the total profit of the N = 50 companies was From the above results = N(Y + nY) N + n a. Calculate the estimate of the total profit using . b. Is this an unbiased estimator for the total profit? Explain. c. Derive an expression for the variance of this estimator (), and calculate the sample standard error. d. Another estimator for the total profit of the 50 companies is * = Y + N, and from the sample i) Calculate the estimate of the total profit using *. ii) Is this an unbiased estimator for the total profit? Explain. iii) Derive an expression for the variance of this estimator, and calculate the sample standard error. a+b is given [Hint: for a random variable and constants, the expected value of a +1 by E(a+b)=a+bE() = a+b, if is unbiased for X . The variance is given by Var(a+b) = bVar()] = 2 = 45 3. The total profit for N = 5 of the largest computer companies was known to be Y = 500 (million dollars). For a sample of n 9 from the remaining N computer companies, the sample mean and the standard deviation were = 30 and S = 15. An estimate suggested for the total profit of the N = 50 companies was From the above results = N(Y + nY) N + n a. Calculate the estimate of the total profit using . b. Is this an unbiased estimator for the total profit? Explain. c. Derive an expression for the variance of this estimator (), and calculate the sample standard error. d. Another estimator for the total profit of the 50 companies is * = Y + N, and from the sample i) Calculate the estimate of the total profit using *. ii) Is this an unbiased estimator for the total profit? Explain. iii) Derive an expression for the variance of this estimator, and calculate the sample standard error. a+b is given [Hint: for a random variable and constants, the expected value of a +1 by E(a+b)=a+bE() = a+b, if is unbiased for X . The variance is given by Var(a+b) = bVar()]