2. Let Y1, Y2, ...,Yn be n pairwise uncorrelated random variables with common me

ID: 3377680 • Letter: 2

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2. Let Y1, Y2, ...,Yn be n pairwise uncorrelated random variables with common mean and common variance 2. Let denote the sample average.

a) define the class of linear estimators of by Wa=a1Y1+a2Y2+...+anYn. Where the ai are constants. What restriction on the ai is needed for Wa to be an unbaised estimator for ?

b) Find Var(Wa)

c) For any numbers a1, a2,...,an, the following inequality holds: (a1 +a2 +...+an)2/n a12 +a22+...+an2. Use this, along with parts a and b, to show that Var(Wa)Var(Y) whenever Wa is unbiased, so that is the best linear estimator. (What does the inequality become when ai satisfy the restriction from part 1)

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2. Let Y1, Y2, ...,Yn be n pairwise uncorrelated random variables with common me

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2. Let Y1, Y2, ...,Yn be n pairwise uncorrelated random variables with common me

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