以ä¸å¼åä¸nC1å°±æ¯n个å1个çç»åæ°ã
å¯ä»¥éæ¨ä¸ä¸ï¼
X=0ï¼P=(n-1/n)*(n-2/n-1)*(n-3/n-2)*â¦â¦*(1/2)*1=(1/n)
X=1: P=nC1*(1/n)*[(n-2/n-1)*(n-3/n-2)*â¦â¦*(1/2)*1]=(1/n-1)
X=2: P=nC2*(1/n)*(1/n-1)*[(n-3/n-2)*(n-4/n-3)*â¦â¦*(1/2)*1]=(1/2n-2)
X=3: P=nC3*(1/n)*(1/n-1)*(1/n-2)*[(n-4/n-3)*(n-5/n-4)*â¦â¦*(1/2)*1]=(1/6n-18)
â¦â¦
设m为å°äºn-1çæ´æ°ï¼åï¼
X=m: P=nCm*(1/n)*(1/n-1)*(1/n-2)*â¦â¦*(1/n-m+1)*[(n-m-1/n-m)*(n-m-2/n-m-1)*â¦â¦*(1/2)*1]=[1/m!(n-m)]
X=n-1: Pä¸åå¨
X=n: P=(1/n)*(1/n-1)*(1/n-2)*â¦â¦*(1/2)*1=(1/n!)
æ以ï¼
E(X)=â[m/m!(n-m)] m=0,1,2,3â¦â¦(n-2)
åå ä¸[1/(n-1)!]
ä¸ä¿è¯æ£ç¡®ã
温馨提示:答案为网友推荐,仅供参考