Question: Consider the sequence of independent and identically distributed random variables X i , i=1,...,5for whichE(X)=3 andVar(X)=3. Consider the following estimator of E(X): X ^ =

Consider the sequence of independent and identically distributed random variables Xi, i=1,...,5for whichE(X)=3 andVar(X)=3.

Consider the following estimator ofE(X):

X^ = 51 X1 + 61 X2 +51X3 +61 X4 +51 X5

  1. Is the estimator X^ positively biased, negatively biased or unbiased?
  2. Is the estimator X^ more, less, or equally as efficient as estimator X =n1 i=15Xi ?

Show all your working and provide all your reasoning.

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