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Omni-MATH / The integers 1,2,3,4,5,6,7,8,9,10 are written on a blackboard. Each day, a teacher chooses one of the integers uniformly at random and decreases it by 1. Let X be the expected valu…

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problem

The integers 1,2,3,4,5,6,7,8,9,101,2,3,4,5,6,7,8,9,10 are written on a blackboard. Each day, a teacher chooses one of the integers uniformly at random and decreases it by 1. Let XX be the expected value of the number of days which elapse before there are no longer positive integers on the board. Estimate XX. An estimate of EE earns ⌊20⋅2−|X−E|/8⌋\left\lfloor 20 \cdot 2^{-|X-E| / 8}\right\rfloor points.
Plain-text mathematical notation (without MathML)
The integers 1,2,3,4,5,6,7,8,9,10 are written on a blackboard. Each day, a teacher chooses one of the integers uniformly at random and decreases it by 1. Let X be the expected value of the number of days which elapse before there are no longer positive integers on the board. Estimate X. An estimate of E earns ⌊20⋅2^(−|X−E|/8)⌋ points.
Original LaTeX notation
The integers \(1,2,3,4,5,6,7,8,9,10\) are written on a blackboard. Each day, a teacher chooses one of the integers uniformly at random and decreases it by 1. Let \(X\) be the expected value of the number of days which elapse before there are no longer positive integers on the board. Estimate \(X\). An estimate of \(E\) earns \(\left\lfloor 20 \cdot 2^{-|X-E| / 8}\right\rfloor\) points.

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task_id
cbeb0d80-9d91-596c-9c0a-7d3531eb8566
task_key
test--cbeb0d80-9d91-596c-9c0a-7d3531eb8566
task_revision_id
1
config / split
/ test

Official source

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