Expected Value of Minimum of $n$ i.i.d. Uniform Random Variable
Given $n$ independent random variables from $\mathcal{U}(0,1)$, what is the expected value of minimum, second minimum, …, maximum of them?
Frequently-used Mathematica Build-in Functions
本文主要记录一下在使用 Mathematica 过程中常用的 build-in functions.
Optimization: Dual Problem and Karush-Kuhn-Tucker Conditions
介绍 Convex Optimization 中的 Dual Problem 和 Karush-Kuhn-Tucker Conditions
Interchanging a limit or a derivative with an integral
本文主要讨论 积分与极限 / 积分与求导 交换顺序。
Monetone Convergence Theorem, Fatou’s Lemma, Dominated Convergence Theorem
本文主要介绍实分析中关于可测函数积分的三大定理：Monetone Convergence Theorem, Fatou’s Lemma, Dominated Convergence Theorem