E2 The scale in Beatrice\'s bathroom gives readings which are normally distribut
ID: 3061548 • Letter: E
Question
E2 The scale in Beatrice's bathroom gives readings which are normally distributed, with mean equal to the weight of the object placed on it, and variance 2, which is unknown, and does not depend on the weight. Beatrice wishes to estimate 2. She places on the scale an object whose weight is known to be exactly 50 lbs, getting a reading Yi. She repeats this independently n-1 times, getting readings y,Y2, ,Yn she is considering the following two estimators of ": B S = (.JX-50)*)/n Her reason for considering the second estimator is that she thinks that since she knows the true weight, she might as well use it, to get more accuracy. Which estimator is better, and does the answer depend on what is the true value of ?Explanation / Answer
The second estimator is more accurate, the reason being that it is the true weight of the object and hence deviations should be taken about that weight. In case n is very large, then mean of the observations is very close to 50 and the two formulas become the same.
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