THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Suppose that x 1 and x 2 are random samples of observations from a population with mean μ and variance σ 2 .Consider the following three point estimators,X,Y,and Z,of μ: X = (x 1 + x 2 )/2,Y = (x 1 + 3x 2 )/4,and Z = (x 1 + 2x 2 )/3.
-Show that all three estimators X,Y,and Z are unbiased.

Question

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The Answer of THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Suppose that x 1 and x 2 are random samples of observations from a population with mean μ and variance σ 2 .Consider the following three point estimators,X,Y,and Z,of μ: X = (x 1 + x 2 )/2,Y = (x 1 + 3x 2 )/4,and Z = (x 1 + 2x 2 )/3.
-Show that all three estimators X,Y,and Z are unbiased.