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In: Statistics and Probability

In estimating the average price of a gallon of gasoline in a region we plan to...

In estimating the average price of a gallon of gasoline in a region we plan to select a random sample (independent and identically distributed) of size 10. Let X1, X2, ... , X10 denote the selected sample. The two estimators for estimating the average price, μ, are:

U1 = (X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8 +X9 + X10)/10
U2 = (X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8 )/8 + X1 - X2 .

a. (6 points) which of the above estimators are unbiased? Fully justify your answer.
b. (14 points) Using the mean square error criterion, determine which estimator is better.

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orchestra answered 1 year ago
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