证:由 x = [x] + {x},知2x = 2[x] + 2{x}. 1.若{x}落在[0,1/2),则2{x} < 1,于是有{2x} = 2{x},此时 {2x} - {x} = {x},落在[0,1/2). 2.若{x}落在[1/2,1),则2{x}落在[1,2),于是{2x} = 2{x} - 1,此时 {2x} - {x} = {x} - 1,落在[-1/2,0). 综上,命题成立.…

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) ADDITIONAL PRACTICE FOR THE FINAL PROBLEM 1 A box contains 8 dark chocolates, 8 milk chocolates, and 8 white chocolates. (It’s amazing how t…

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 Zeros and Ones: Sum of a sample with replacement $S$ is the number of successes: $n$ independent trials, chance of success on a sing…

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 Standard Error The standard error of a random variable $X$ is defined by $$SE(X)=\sqrt{E((X-E(X))^2)}$$ $SE$ measures the rough size…

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…

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) PRACTICE PROBLEMS FOR THE MIDTERM PROBLEM 1 In a group of 5 high school students, 2 are in 9th grade, 2 are in 10th grade, and 1 is in 12th…

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 Independent $$P(A\cap B)=P(A)\cdot P(B)$$ Binomial Distribution $$C_{n}^{k}\cdot p^k\cdot(1-p)^{n-k}$$ R function: dbinom(k, n, p) U…

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 Bayes Theorem $$P(A_i|B)=\frac{P(B|A_i)\cdot P(A_i)}{\sum_{j}P(B|A_j)\cdot P(A_j)}$$ where $$P(B)=\sum_{j}P(B|A_j)\cdot P(A_j)$$ GRA…

开发中,例如: nanshanImage.image=[UIImage imageNamed:@'index_pic.png']; 在项目中还保存中index_pic@2x.png的图片,此图为了只适应960*640的分辨率手机 注意:适应Iphone5的相关图片尺寸,也要加@2x.png.比如欢迎界面:Default-568h@2x.png:这个才能匹配上. 而index_pic.png是适应640*320的手机,但是在代码中必须写成[UIImage imageNamed:@'index_pi…

从新注册 .DLL  CMD 运行regsvr32  *.dll注册该DLL  或 regsvr32 /s  *.DLL 求证…