每个大学教材上都会提到这个定理,枯燥地给出了定义和公式,并没有解释来龙去脉,导致大多数人望而生畏,并没有理解它的美. <女士品茶>有感 待续~ 参考:怎样理解和区分中心极限定理与大数定律?…

大数定律 Law of large numbers (LLN) 虽然名字是 Law,但其实是严格证明过的 Theorem weak law of large number (Khinchin's law) The weak law of large numbers: the sample average converges in probability to the expected value $\bar{X_n}=\frac{1}{n}(X_1+ \cdots +X_n) \overset{…

title: [概率论]6-2:大数定理(The Law of Large Numbers) categories: - Mathematic - Probability keywords: - Markov Inequality - Chebyshev Inequality - Sample Mean - The Law of Large Numbers toc: true date: 2018-04-07 21:07:42 Abstract: 本文介绍马尔科夫不等式,切比雪夫不等式,样本均值…

大数定律:每次从总体中随机抽取1个样本,这样抽取很多次后,样本的均值会趋近于总体的期望.也可以理解为:从总体中抽取容量为n的样本,样本容量n越大,样本的均值越趋近于总体的期望.当样本容量极大时,样本均值 . (注:总体数据需要独立同分布) 下图展示的是:每次从1,2,3当中随机选取一个数字,随着抽样次数的增加,样本均值越来越趋近于总体期望((1+2+3)/3=2). 大数定律的作用:可以用样本均值来估计总体的期望.…

https://www.math.wustl.edu/~russw/f10.math493/chebyshev.pdf http://www.tkiryl.com/Probability/Chapter%208.pdf http://mathworld.wolfram.com/ChebyshevInequality.html Apply Markov's inequality with  to obtain (1) Therefore, if a random variable  has a f…

uva10392 Factoring Large Numbers 本文涉及的知识点是,使用线性筛选法得到素数表. Table of Contents 1 题目 2 思路 3 参考 1 题目 ==================== Problem F: Factoring Large Numbers One of the central ideas behind much cryptography is that factoring large numbers is computationall…

When looking at large numbers in code (such as 1800000) it’s oftentimes difficult for the human eye to quickly see how big the number actually is. TypeScript allows us to use numeric separators to write numbers in a more human readable format (such a…

概率基础和R语言 R的极客理想系列文章,涵盖了R的思想,使用,工具,创新等的一系列要点,以我个人的学习和体验去诠释R的强大. R语言作为统计学一门语言,一直在小众领域闪耀着光芒.直到大数据的爆发,R语言变成了一门炙手可热的数据分析的利器.随着越来越多的工程背景的人的加入,R语言的社区在迅速扩大成长.现在已不仅仅是统计领域,教育,银行,电商,互联网….都在使用R语言. 要成为有理想的极客,我们不能停留在语法上,要掌握牢固的数学,概率,统计知识,同时还要有创新精神,把R语言发挥到各个领域.让我们一起…

"generative algorithm models how the data was generated in order to categorize a signal. It asks the question: based on my generation assumptions, which category is most likely to generate this signal?discriminative algorithm does not care about how…

Dictum:  Nutrition books in the world. There is no book in life, there is no sunlight; wisdom without books, as if the birds do not have wings. -- Shakespeare 蒙特卡洛(Monte Carlo, MC)方法是一种不基于模型的方法.它不需要具有完备的环境知识,只要求具备经验,即来自于真实的或模拟的环境交互过程中的样本序列\(\{\mathca…