Suppose that Y1, Y2,..., Yn is a random sample from a normal distribution with mean and

Chapter 9, Problem 9.5

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QUESTION:

Suppose that Y1, Y2,..., Yn is a random sample from a normal distribution with mean and variance 2. Two unbiased estimators of 2 are 2 1 = S2 = 1 n 1 n i=1 (Yi Y ) 2 and 2 2 = 1 2 (Y1 Y2) 2 . Find the efficiency of 2 1 relative to 2 2 .

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QUESTION:

Suppose that Y1, Y2,..., Yn is a random sample from a normal distribution with mean and variance 2. Two unbiased estimators of 2 are 2 1 = S2 = 1 n 1 n i=1 (Yi Y ) 2 and 2 2 = 1 2 (Y1 Y2) 2 . Find the efficiency of 2 1 relative to 2 2 .

ANSWER:

Step 1 of 4

Given:

The random sample  follows normal distribution with mean and variance .

The two unbiased estimators are,

   and  

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