Mathematics, 28.05.2021 14:00 neariah24

Let X1, · · · , X4 denote a random sample from a population having mean µ and variance σ^ 2 = 1. Consider the following estimators of µ: θ1 = (X1 + X2 + X3 + X4)/ 4 ,
θ2 = (2X1 − X2 + X3 ) / 2 .
(a) (5 points) Show whether or not each estimator is unbiased.
(b) (5 points) Calculate V (θb1) and V (θb2). Which estimator is better? Why?

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Let X1, · · · , X4 denote a random sample from a population having mean µ and variance σ^ 2 = 1. Con...

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