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Questions › DSE › DSE 2011 › Q40
2 marksStatistics › Random variables and standard distributions › Expectation and varianceHardabout 4 min

DSE 2011 Question 40: Random variables and standard distributions

A student may take a test at most thrice. Each time, his score is an independent draw from the uniform distribution on [0,100][0,100][0,100]. After learning a score, he can stop and accept it, or discard it and retake; if he rejects twice, the third score is final. To maximize his expected official score, the student will decide to be retested after the very first test if and only if his score is less than

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A student may take a test at most thrice. Each time, his score is an independent draw from the uniform distribution on [0,100]. After learning a score, he can stop and accept it, or discard it and retake; if he rejects twice, the third score is final. To maximize his expected official score, the student will decide to be retested after the very first test if and only if his score is less than (A) 50 (B) 62.5 (C) 75 (D) 87.5

Random variables and standard distributions has come up 173 times in 7 exams since 2005.

What this question tests

This question is on Expectation and variance, part of Random variables and standard distributions in Statistics.

The mean and spread of a random variable, and how they change under transformations and sums.

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Question from the DSE 2011 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.