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…

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 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{…

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: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.…

关键:添加English,并上移到第一,即开机默认即可.Win8+不用修改注册表的,只有win7里才可能需要修改注册表. http://superuser.com/questions/327479/ctrl-space-always-toggles-chinese-ime-windows-7 Stack Exchange Inbox Reputation and Badges sign up log in tour help Super User Questions Tags Users Bad…

原文:Introduction todnorm,pnorm,qnorm, andrnormfor new biostatisticians Today I was in Dan’s office hours and someone asked, “what is the equivalent in R of the back of the stats textbook table of probabilities and their corresponding Z-scores?” (This …

连续(Continuity) 所有点连续   ->   一致连续 (uniform continuity)  ->  绝对连续  -> 李普希兹连续(Lipschitz) 弱                    ---->               强 [uniform continutity] In mathematics, a function f is uniformly continuous if, roughly speaking, it is possible to…

Nice R Code Punning code better since 2013 RSS Blog Archives Guides Modules About Markov Chain Monte Carlo 10 JUNE 2013 This topic doesn’t have much to do with nicer code, but there is probably some overlap in interest. However, some of the topics th…

Stat2.2x Probability(概率)课程由加州大学伯克利分校(University of California, Berkeley)于2014年在edX平台讲授. PDF笔记下载(Academia.edu) Summary Law of Large Numbers As the number of trials increases, the chance that the proportion of successes is in the range $$p\pm\text{a fi…