一个概率题

Eastsun

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

问的问题呢？只给出规则，怎么没有问的问题？

Eastsun

囧，把题目补充完整了

mathe

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？