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[zz]概率论感觉测试(答案)

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谢谢大家提出的建议。我改了一些这里的小错误。

1.  假设考试周为1个礼拜(周一到周日),且考试时间为均匀分布,假使你有3门考试,则最后一门考试大约在

A. 周五
B. 周六
C. 周日

Answer: B. 一般的讲在[0,1]之间n个均匀分布的随机变量最大值期望为n/(n+1), 也就是可以认为这n个随机变量分别大约在 1/(n+1), 2/(n+1),…, n(n+1)。这道题那么算一下大概就是在周六的上午。

2. 如果你去参与一项赌博,每次的回报为正态分布,假设你赌了100把发现赢了10000块(明显是很小概率事件,但假设确实发生了),那么你觉得你最有可能是因为

A. 有一把赢了很多
B. 一直在慢慢的赢
C. 两种情况都有可能

Answer: B. 也许答案对很多人有些出乎意料。在这种情况下,可能一般觉得能够连续赢很多把很难,但是实际上赢一把大的更难。这个问题是随机变量的长尾还是短尾的问题。长尾的意思就是取离均值很远的概率不是很小,而短尾正好相反。题目中的正态分布属于短尾,因为密度函数是按照平方的指数下降的,如果稍微改一下题目中的分布,则有可能是因为一次赢了很大而最后赢的。另外说一句,有一本书叫《长尾理论》,里面说明了现在的经济中有很多东西是长尾的,比如说一年销量排在100000名之后的歌曲仍然能占据市场的一部分。这是电子商务流行的很重要原因,因为不必支付储存这个长尾的cost。

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Written by apollozhao

2013/05/18 at 12:12

[zz]概率论与数理统计公式大全

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第一章  随机事件和概率 

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Written by apollozhao

2012/09/14 at 08:43

[zz]再议统计生统经典书目

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from: http://blog.renren.com/share/223421102/3831395253#continueread

 

发现本科的统计即使学完了也非常粗浅,更何况没有好好学。下决心好好看一些大师之作。
Probability & Measure:
Probability Theory: Theory and Examples, 3rd edition, Richard Durrett 国内有第2版影印本
Probability and Measure, Patrick Billingsley
Convergence of Probability Measures, Patrick Billingsley
A Course in Probability Theory Revised, Kai Lai Chung
Mathematical Statitsics:
Introduction to Mathematical Statistics, Hogg & Craig (高教社出了第5版影印本)
Mathematical Statistics, Jun Shao
Mathematical Statistics, Peter J. Bickle
作为数理统计学的课本不错。茆诗松、王静龙的《高等数理统计》是国内用得很多的课本。
Inference:
Statistical Inference, Casella & Berger 是国外读统计基本必修的的一本书,国内有影印本。All of Statistics: A Concise Course in Statistical Inference, Larry Wasserman 是一本涵盖面很广的速成式的lecture notes样式的书,偏nonparametric。Theory of Statistics, Schervish 偏Bayesian和decision theory。此外还有: Testing Statistical Hypotheses, Lehmann & Romano, Theory of Point Estimation, Lehmann & Casella。更多的advanced topics举不胜举。
Asymptotics & large sample theory:
A Course in Large Sample Theory, Ferguson 是很好的教本,
Asymptotic Statistics, A. W. van der Vaart
Elements of Large Sample Theory, Lehmann
Approximation Theorems of Mathematical Statistics, Serfling

Linear Models & Regression:
Applied Linear Statistical Models, Kutner et al 或者 Introduction to Linear Regression Analysis, 3ed. Montgomery, Peck, Vining可以作为入门的Regression的教本。
C. R. Rao的Linear Statistical Inference and Its Application很值得看一看。Linear Regression Analysis, Seber & Lee写得也不错。国内写得很不错的教本是王松桂写的《线性模型引论》,科学出版社,但是稍有一些错误。

Generalized Linear Models数McCullagh & Nelder 最经典,入门可以用An Introduction to Generalized Linear Models, 3ed, Dobson & Barnett。
Generalized Linear Models: A Bayesian Perspective, Dey, Ghosh, Mallick
Categorical Data Analysis, Agresti是Categorical的经典。SAS和R做Categorical的手册都有出版,对于应用统计的research来说Categorical是很基本的。

Generalized, Linear, and Mixed Models, McCulloch & Seale
Linear Mixed Models for Longitudinal Data, Verbeke & Molenberghs
Semiparametric Regression, Ruppert, Wand, Carroll里面把nonpar & semipar和mixed model统一起来
SAS for Mixed Models, 2ed 和 Mixed Effects Models in S and S-Plus, Pinheiro & Bates 实现
An Introduction to Multivariate Statistical Analysis, T.W. Anderson
Aspects of Multivariate Statistical Theory, Muirhead
Applied Multivariate Statistical Analysis, 6ed, Johnson and Wichern 国内有第6版影印本
Bayesian Data Aanlysis, Gelman, Carlin, Stern, Rubin
Bayesian Methods for Data Analysis, 3rd edition, Carlin & Louis
Statistical Decision Theory and Bayesian Analysis, James O. Berger
Theory of Statistics, Schervish
The Bayesian Choice, Christian P. Robert
Bayesian Theory, Bernardo & Smith
Generalized Linear Models: A Bayesian Perspective, Dey, Ghosh, Mallick
MCMC比较好的书有
Markov Chain Monte Carlo in Practice, Gilks & Richardson & Spiegelhalter
Monte Carlo Strategies in Scientific Computing, Jun S. Liu
Monte Carlo Statistical Methods, Robert & Casella
Nonparametric & Semiparametric:
Semiparametric Regression, Ruppert, Wand, Carroll
Applied Nonparametric Regressions, Wolfgang Härdle
Nonparametric and Semiparametric Models, Wolfgang Härdle et al
Efficient and Adaptive Estimation for Semiparametric Models, Bickel et al
All of Nonparametric Statistics, Larry Wasserman
Nonparametrics: Statistical Methods Based on Ranks, Erich L. Lehmann
Generalized Additive Models, Hastie & Tibshirani
此外,推荐 Empirical Likelihood, Owen
Analysis of Longitudinal Data, Diggle, Heagerty, Liang, Zeger
Applied Longitudinal Analysis, Fitzmaurice, Laird, Ware
Linear Mixed Models for Longitudinal Data, Verbeke & Molenberghs
Missing Data & Causal Inference 比较好的书有
Statistical Analysis with Missing Data 2ed, Little & Rubin
Missing Data in Clinical Studies, Molenberghs & Kenward
Semiparametric Theory and Missing Data, Tsiatis
Applied Bayesian Modeling and Causal Inference from Incomplete-Data Perspectives这本书是Rubin这派几代人对causal inference的一个集成
Robins这派的东西就看paper吧,Robins & Morgan 09年也会出一本书
Unified Methods for Censored Longitudinal Data and Causality, Van der Laan & Robins
Missing Data in Longitudinal Studies, Daniels & Hogan
Bradley Efron写的2本书和Peter Hall的1本是Bootstrap的经典,
Bootstrap Methods and Their Application, Davison & Hinkley
Survival Analysis:
Counting Processes and Survival Analysis, Fleming & Harrington 非常难读但是确实非常经典
Survival Analysis: Techniques for Censored and Truncated Data. Klein & Moeschberger
Modeling Survival Data: Extending the Cox Model, Therneau & Grambsh 有大量的technique
The Statistical Analysis of Failure Time Data, Kalbfleisch & Prentice 第一版里处处有一些很好的idea,第二版又全面总结了近年的research development
Modelling Survival Data in Medical Research, 2nd edition, David Collett
SAS实现用Survival Analysis Using the SAS: A Practical Guide, Paul D. Allison
subtopics:
Analysis of Multivariate Survival Data, Hougaard
Bayesian Survival Analysis, Ibrahim, Chen, Sinha
Functional Data Analysis, Ramsay & Silverman

Elements of Statistical Learning, Hastie, Tibshirani, Friedman
Xiao-Hua Zhou的Statistical Methods in Diagnostic Medicine和Margaret Sullivan Pepe的The Statistical Evaluation of Medical Tests for Classification and Prediction是Diagnostic Test的经典。也有人用Bayesian方法做Clinical Trials的,可以在Bayesian Approaches to Clinical Trials and Health-Care Evaluation里面看到,作者是Spiegelhalter, Abrams, Myles.
一本极好的书叫《女士品茶:20世纪统计怎样变革了科学》(The Lady Tasting Tee: How Statistics Revolutionized Science in the Twentieth Century),希望学习统计的都去看看。里面从Francis Galton, Karl Pearson, R. A. Fisher,讲到Jerzy Neyman, Emil J. Gumbel, Abraham Wald,Wassily Hoeffding, John Tukey, Florence David Nightingale, Frank Wilcoxon, L.J. Savage, George W. Snedecor, William Cochran, Gertrude Cox, Samuel Wilks, Henry Carver, I.J. Good, Bradley Efron, George Box的经历. 内容多为一些统计思想的原型,还有许多奇闻轶事。


希望大家多多补充!

 

 

 

 

源地址:http://blog.renren.com/GetEntry.do?id=327260584&owner=238603604

Written by apollozhao

2010/11/02 at 12:20