THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION

question 134

Essay

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Suppose that x₁ and x₂ are random samples of observations from a population with mean μ and variance σ².Consider the following three point estimators,X,Y,and Z,of μ: X = (x₁ + x₂)/2,Y = (x₁ + 3x₂)/4,and Z = (x₁ + 2x₂)/3.
-Show that all three estimators X,Y,and Z are unbiased.

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Definitions:

Reconstruction

Reconstruction refers to the period following the Civil War (1865-1877) in which the United States attempted to redress the inequities of slavery and its political, social, and economic legacy and to solve the problems arising from the readmission to the Union of the 11 states that had seceded.

Republican Party

One of the two major political parties in the United States, historically associated with the abolition of slavery and civil rights, although its political stance has evolved over time.

U.S. Supreme Court

The highest court in the United States, serving as the final arbiter of legal disputes and constitutional matters.

Federal Government

The national government of a federal country, where powers are divided between the central authority and constituent political units (states or provinces).