then lulhent is true, then prove it, and if it is false, then explain why in why

Question

then lulhent is true, then prove it, and if it is false, then explain why in why it's false E2 The scale in Beatrice's bath room gives readings which are normally distributed, with mean equal to the weight of the object pl does not depend on the weight. Beatrice wishes to estimate o. She places on thes an object whose weight is known to be exactly 50 Ibs. getting a reading Y,. She repeals this independently n - 1 times. getting readings .. She is considering aced on it, and variance 2, which is unknown, a following two estimators of a. 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. does the answer depend on what is the true value of ? Which estimator is better, and

Explanation / Answer

Solution-

Although true mean value is known in the estimator B, but this is not sufficient for that estimator to be called better. Estimator A is an unbiased estimator and thus should be considered over the other. If the sample size is large, then knowing actual mean value may not be a big help as sample mean would approach true mean as per law of large numbers.

In a nutshell, Estimator A should be considered because it is an unbiased estimator.

Thanks!

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