Jensen

Jensen 不等式定义 若 \(f(x)\) 为区间 \(I\) 上的下凸函数，则对于任意 \(x_{i} \in I\) 和满足 \(\displaystyle\sum_{i=1}^{n} \lambda_{i} = 1\) 的 \(\lambda_{i} \gt 0 \left( i = 1, ......

````python #!/usr/bin/env python3 # -*- coding: utf-8 -*- """ Created on Fri Jun 26 16:05:57 2020 @author: vkchlt0297 """ from matplotlib import pyplo ......

$$ f(E[x]) \leq E[f(x)]$$ where $f(x)$ is a convex function. This just a general form of convexity since $E(x)$ is a linear conbination of x. ......