共有球1+2+3+...+n=n(n+1)/2只.
1²+2²+...+n²=n(n+1)(2n+1)/6
分布列
X 1 2 ...k ...n
P 1/[n(n+1)/2] 2/[n(n+1)/2] ...k/[n(n+1)/2] ...n/[n(n+1)/2]
EX=2(1²+2²+...+n²)1/[n(n+1)/2]=(2n+1)/3.
共有球1+2+3+...+n=n(n+1)/2只.
1²+2²+...+n²=n(n+1)(2n+1)/6
分布列
X 1 2 ...k ...n
P 1/[n(n+1)/2] 2/[n(n+1)/2] ...k/[n(n+1)/2] ...n/[n(n+1)/2]
EX=2(1²+2²+...+n²)1/[n(n+1)/2]=(2n+1)/3.