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a. Calculate the estimate of the total profit using Ŷ. b. Is this an unbiased estimator for the total profit? Explain. c. Derive an expression for the variance of this estimator (Ŷ), and calculate the sample standard error. d. Another estimator for the total profit of the 50 companies is Ŷ* = Y₁ + N₂Ŷ₂, and from the sample i) Calculate the estimate of the total profit using Ŷ*. 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. Calculate the estimate of the total profit using Ŷ. b. Is this an unbiased estimator for the total profit? Explain. c. Derive an expression for the variance of this estimator (Ŷ), and calculate the sample standard error. d. Another estimator for the total profit of the 50 companies is Ŷ* = Y₁ + N₂Ŷ₂, and from the sample i) Calculate the estimate of the total profit using Ŷ*. 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.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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= 3. The total profit for N₁ = 5 of the largest computer companies was known to be Y₁ = 500 (million dollars). For a sample of n₂ 9 from the remaining N₂ = 45 computer companies, the sample mean and the standard deviation were Y₂ = 30 and S₂ = 15. An estimate suggested for the total profit of the N = 50 companies was N(Y₁ + n₂Ŷ₂) N₁ + 1₂ Ŷ = From the above results a. Calculate the estimate of the total profit using Ŷ. b. Is this an unbiased estimator for the total profit? Explain. c. Derive an expression for the variance of this estimator (Ŷ), and calculate the sample standard error. d. Another estimator for the total profit of the 50 companies is Ŷ* = Y₁ + N₂Ŷ₂, and from the sample i) Calculate the estimate of the total profit using Ŷ*. 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. [Hint: for a random variable and constants, the expected value of a+by is given by E(a+bÂ)=a+bE(Î) = a +bX, if ✰ is unbiased for X . The variance is given by Var(a+bẪ)=b²Var(Â)I
Transcribed Image Text:= 3. The total profit for N₁ = 5 of the largest computer companies was known to be Y₁ = 500 (million dollars). For a sample of n₂ 9 from the remaining N₂ = 45 computer companies, the sample mean and the standard deviation were Y₂ = 30 and S₂ = 15. An estimate suggested for the total profit of the N = 50 companies was N(Y₁ + n₂Ŷ₂) N₁ + 1₂ Ŷ = From the above results a. Calculate the estimate of the total profit using Ŷ. b. Is this an unbiased estimator for the total profit? Explain. c. Derive an expression for the variance of this estimator (Ŷ), and calculate the sample standard error. d. Another estimator for the total profit of the 50 companies is Ŷ* = Y₁ + N₂Ŷ₂, and from the sample i) Calculate the estimate of the total profit using Ŷ*. 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. [Hint: for a random variable and constants, the expected value of a+by is given by E(a+bÂ)=a+bE(Î) = a +bX, if ✰ is unbiased for X . The variance is given by Var(a+bẪ)=b²Var(Â)I
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