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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Let X1,X2,X3,and X4 be a random sample of observations from a population with mean μ and variance σ2.Consider the following two point estimators of μ: THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Let X<sub>1</sub>,X<sub>2</sub>,X<sub>3</sub>,and X<sub>4</sub> be a random sample of observations from a population with mean μ and variance σ<sup>2</sup>.Consider the following two point estimators of μ:    <sub>1</sub> = 0.10 X<sub>1</sub> + 0.40 X<sub>2</sub> + 0.40 X<sub>3</sub> + 0.10 X<sub>4</sub> and    <sub>2</sub> = 0.20 X<sub>1</sub> + 0.30 X<sub>2</sub> + 0.30 X<sub>3</sub> + 0.20 X<sub>4</sub> -Which of the following statements is true? A)     <sub>1</sub> is biased,but     <sub>2</sub> is an unbiased estimator of μ. B)     <sub>1</sub> is unbiased,but     <sub>2</sub> is a biased estimator of μ. C) Both    <sub>1</sub> and     <sub>2</sub> are unbiased estimators of μ. D) Both    <sub>1</sub> and     <sub>2</sub> are biased estimators of μ.
1 = 0.10 X1 + 0.40 X2 + 0.40 X3 + 0.10 X4 and THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Let X<sub>1</sub>,X<sub>2</sub>,X<sub>3</sub>,and X<sub>4</sub> be a random sample of observations from a population with mean μ and variance σ<sup>2</sup>.Consider the following two point estimators of μ:    <sub>1</sub> = 0.10 X<sub>1</sub> + 0.40 X<sub>2</sub> + 0.40 X<sub>3</sub> + 0.10 X<sub>4</sub> and    <sub>2</sub> = 0.20 X<sub>1</sub> + 0.30 X<sub>2</sub> + 0.30 X<sub>3</sub> + 0.20 X<sub>4</sub> -Which of the following statements is true? A)     <sub>1</sub> is biased,but     <sub>2</sub> is an unbiased estimator of μ. B)     <sub>1</sub> is unbiased,but     <sub>2</sub> is a biased estimator of μ. C) Both    <sub>1</sub> and     <sub>2</sub> are unbiased estimators of μ. D) Both    <sub>1</sub> and     <sub>2</sub> are biased estimators of μ.
2 = 0.20 X1 + 0.30 X2 + 0.30 X3 + 0.20 X4
-Which of the following statements is true?


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