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…

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) 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) 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) 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…

Stat2.3x Inference(统计推断)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 In the following problems you will be asked to choose one of the four options (A)-(D). The options are sta…

Stat2.3x Inference(统计推断)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 Test of Hypotheses $$\text{Null}: H_0$$ $$\text{Alternative}: H_A$$ Assuming the null is true, the chance of getting data like the d…

Stat2.3x Inference(统计推断)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 Estimating population means and percents Sampling assumptions: Simple Random Sample (SRS) Large enough so that the probability histo…