5.2.4hard一级题目发布者: ai-batch题干记 xˉn=1n∑i=1nxi\bar{x}_n = \frac{1}{n} \sum_{i=1}^{n} x_ixˉn=n1∑i=1nxi，sn2=1n−1∑i=1n(xi−xˉn)2s_n^2 = \frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x}_n)^2sn2=n−11∑i=1n(xi−xˉn)2，n=1,2,…n = 1, 2, \ldotsn=1,2,…，证明： xˉn+1=xˉn+1n+1(xn+1−xˉn),\bar{x}_{n+1} = \bar{x}_n + \frac{1}{n+1} (x_{n+1} - \bar{x}_n),xˉn+1=xˉn+n+11(xn+1−xˉn), sn+12=n−1nsn2+1n+1(xn+1−xˉn)2.s_{n+1}^2 = \frac{n-1}{n} s_n^2 + \frac{1}{n+1} (x_{n+1} - \bar{x}_n)^2.sn+12=nn−1sn2+n+11(xn+1−xˉn)2.