Let Y1, Y2, Y3, and Y4be independent, identically distributed random variables from a population with a...

Let Y₁, Y₂, Y₃, and Y₄be independent, identically distributed random variables from a population with a mean μ and a variance σ^2. Consider a different estimator of μ:

W = Y₁+ Y₂+ Y₃+ Y_4.

Let Y₁, Y₂, Y₃, and Y₄be independent, identically distributed random variables from a population with a mean μ and a variance σ^2. Consider a different estimator of μ:

W = 1/8 Y₁+ 1/3 Y₂+ 1/6 Y₃+ 3/8 Y_4.

This is an example of a weighted average of the Y_i.

Show that W is a linear estimator.
IsW an unbiased estimator of μ? Show that it is – or it isn’t (E(W) = ?).
Find the variance of Wand compare it to the variance of the sample mean .
IsW as good an estimator as y̅? Explain your answer.

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Expert Solution

orchestra answered 1 year ago

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