題組內容

2. Suppose that 61c9548147dd1.jpg are n random variables that are drawn independently from a population that is normally distributed with a mean u and variance σ2. n is an even number. A researcher is considering three alternative estimators of the population mean p. The first estimator is:
61c954bf140cc.jpg
The second estimator is:
61c954d1147f0.jpg
here, we assume that n is an even number and only the odd numbered X's are included in the estimator. For instance, if n = 10 and the estimator is:61c954ecba4b8.jpg =
61c9550402bb6.jpg. The third estimator is:
61c955135292b.jpg

(b) Which one is relatively more effcient? Explain and show your work.