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HMMT 二月 2018 · 冲刺赛 · 第 34 题

HMMT February 2018 — Guts Round — Problem 34

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 20 ] 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 . −| X − E | / 8 An estimate of E earns b 20 · 2 c points.
解析
  1. [ 20 ] 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 . −| X − E | / 8 An estimate of E earns b 20 · 2 c points. Proposed by: Mehtaab Sawhney Answer: 120 . 75280458176904 29673761980310360290435187545023378925682165679114151937768966599764336431473191952862689256885663426948