Question

In: Statistics and Probability

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 σ2.  Consider a different estimator of μ:

W =  Y1+  Y2+ Y3+ Y4.

Let Y1, Y2, Y3, and Y4be independent, identically distributed random variables from a population with a mean μ and a variance σ2.  Consider a different estimator of μ:

W = 1/8 Y1+ 1/3 Y2+ 1/6 Y3+ 3/8 Y4.

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

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

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