hdu-5810 Balls and Boxes(概率期望)

题目链接：

Balls and Boxes

Time Limit: 2000/1000 MS (Java/Others)    

Memory Limit: 65536/65536 K (Java/Others)

Problem Description

Mr. Chopsticks is interested in random phenomena, and he conducts an experiment to study randomness. In the experiment, he throws n balls into m boxes in such a manner that each ball has equal probability of going to each boxes. After the experiment, he calculated the statistical variance V as

V=∑mi=1(Xi−X¯)2m

where Xi is the number of balls in the ith box, and X¯ is the average number of balls in a box.
Your task is to find out the expected value of V.

 

 

Input

The input contains multiple test cases. Each case contains two integers n and m (1 <= n, m <= 1000 000 000) in a line.
The input is terminated by n = m = 0.

 

 

Output

For each case, output the result as A/B in a line, where A/B should be an irreducible fraction. Let B=1 if the result is an integer.

 

 

Sample Input

2 1

2 2

0 0

 

 

Sample Output

0/1

1/2

 

题意：

 

把n个球放到m个盒子里面,求上面这个式子的期望;

 

思路：

 

推期望公式的题,我推的过程跟题解的不太一样;

 

E(V)=1/m*E(∑(x _i-x) ²)=E((x-n/m) ²)=E(x ²)-2*n/m*E(x)+n ²/m ²

E(x)=n/m;E(x ²)=D(x)+[E(x)] ²;变成二项分布了,D(x)=n*(m-1)/m ²

所以带到上面的式子中就变成了E(v)=n*(m-1)/m ²

 

AC代码：

 

#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 

　　

转载于:https://www.cnblogs.com/zhangchengc919/p/5755050.html