Let X1, X2, X3, and X4 be a random sample of observations from a population with

Q: Let X1, X2, X3, and X4 be a random sample of observations from a population with

Solution D. Both 1 and 2 are unbiased estimators of E(1) = E(0.1X1+0.4X2+0.4X3+0.1X4) = 0.1 +0.4 +0.4 +0.1 = E(2) = E(0.2X1+0.3X2+0.3X3+0.2X4) = 0.2 + 0.3 +0.3 +0.0 = Therefore both the estimators are unbiased

ID: 3353457 • Letter: L

Question

Let X1, X2, X3, and X4 be a random sample of observations from a population with mean and variance 2. The observations are independent because they were randomly drawn. Consider the following two point estimators of the population mean : 1 = 0.10 X1 + 0.40 X2 + 0.40 X3 + 0.10 X4 and 2 = 0.20 X1 + 0.30 X2 + 0.30 X3 + 0.20 X4 Which of the following statements is true? A. 1 is unbiased, but 2 is a biased estimator of . B. 1 is biased, but 2 is an unbiased estimator of . C. Both 1 and 2 are biased estimators of . D. Both 1 and 2 are unbiased estimators of .

Explanation / Answer

Solution

D. Both 1 and 2 are unbiased estimators of

E(1) = E(0.1X1+0.4X2+0.4X3+0.1X4) = 0.1 +0.4 +0.4 +0.1 =

E(2) = E(0.2X1+0.3X2+0.3X3+0.2X4) = 0.2 + 0.3 +0.3 +0.0 =

Therefore both the estimators are unbiased

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Let X1, X2, X3, and X4 be a random sample of observations from a population with

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