DSE 2016 Question 28: Random variables and standard distributions
Setup, from Q27 of the paper:
A student may take a test at most three times. Each attempt's score is an independent draw from the uniform distribution on [0,100]. After seeing a score she may stop and accept it or discard it and retake; after the third attempt she must accept the third score. She maximises her expected official score. Following an optimal plan, her expected score before taking any test is approximately:
(Same three-attempt test as the previous question, scores i.i.d. uniform on [0,100].) Now the university allows the third (final) test only if the second-test score is below 40. The student may still stop or retake after the first attempt. She decides to be retested after the first test if and only if her first score is less than:
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Plain-text version
Setup, from Q27 of the paper: A student may take a test at most three times. Each attempt's score is an independent draw from the uniform distribution on [0,100]. After seeing a score she may stop and accept it or discard it and retake; after the third attempt she must accept the third score. She maximises her expected official score. Following an optimal plan, her expected score before taking any test is approximately: (Same three-attempt test as the previous question, scores i.i.d. uniform on [0,100] .) Now the university allows the third (final) test only if the second-test score is below 40. The student may still stop or retake after the first attempt. She decides to be retested after the first test if and only if her first score is less than: (A) 37.5 (B) 50 (C) 62 (D) 67.5
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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