题目
Group A consists of the values and Group B consists of .
(a) Compute the mean of each group.
(b) Now move the element from Group B to Group A. Recompute the mean of each group. Verify that both means have increased.
(c) The overall mean across all 8 values is unchanged. Prove the following general statement: if an element is moved from group B to group A, and the element's value satisfies (where are the pre-move group means), then both post-move group means strictly exceed their pre-move values.
(d) A medical study reports that a new diagnostic technology has improved average survival time in both Stage I and Stage II cancer patients, yet overall survival is unchanged. Explain how this is possible without any actual improvement in treatment.
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你的答案
a.mean_A
a.mean_B
b.mean_A_prime
b.mean_B_prime
b.means_increased_verification
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A fund-of-funds manager reclassifies a hedge fund strategy from the 'relative value' bucket to the 'macro' bucket. The fund's Sharpe ratio is 0.8, while the pre-move average Sharpe is 0.5 for macro and 1.2 for relative value. Show that this single reclassification raises the reported average Sharpe ratio of both buckets. Discuss how this creates misleading performance reporting.
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