一个概率题

Eastsun · 发表于 2008-10-25 16:24:13

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首先推荐一个网站：Project Euler

What is Project Euler? Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. Although mathematics will help you arrive at elegant and efficient methods, the use of a computer and programming skills will be required to solve most problems.

问题(213题) A 30*30 grid of squares contains 900 fleas, initially one flea per square. When a bell is rung, each flea jumps to an adjacent square at random (usually 4 possibilities, except for fleas on the edge of the grid or at the corners). What is the expected number of unoccupied squares after 50 rings of the bell? PS:囧，copy的时候掉了一截 [ 本帖最后由 Eastsun 于 2008-10-25 16:37 编辑 ]

mathe · 发表于 2008-10-25 16:33:40

问的问题呢？只给出规则，怎么没有问的问题？

Eastsun · 发表于 2008-10-25 16:38:33

囧，把题目补充完整了

mathe · 发表于 2008-10-25 17:38:50

题目不难。推广一下，m*n的格子，开始每格一只跳蚤。问经过k步以后，空格的期望数目是多少？如果k趋向无穷，极限是否存在，如果存在是多少？

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[转载] 一个概率题

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