Eastsun 发表于 2008-10-25 16:24:13

一个概率题

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:handshake

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?:lol
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