MIT600SC笔记14&15



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第十四课:Sampling and Monte Carlo Simulation

骰子问题

Monte Carlo simulation—>Inferential statistics(random sample tends to exhibit the same properties as the population)

Bernoulli’s law (law of large numbers)

Repeated independent tests with the same actual probability, p Chance that fraction of times outcome  occurs converges to p as numbers trials goes to infinity.)

第十五课:Statistical Thinking

翻硬币,有正确的结果不代表我们的想法是正确的

How many samples are needed to have confidence in results?

variance — measure of how much spread there is in possible outcomes.

standard deviation标准偏差测量 — the fraction of values close to mean (计算公式如下)formula15-1

 

Coefficient of variation 变异系数– standard deviation by the mean (如果平均数接近0,细微的改变也会造成巨大变化,要三思)

If < 1,  low variance

变异系数can’t be used for confidence intervals, 标准差可以

normal distribution正态分布 peaks at mean, falls of symmetrically

正态分布常用来构造概率模型的原因:

1) Nice mathematical properties

2) Many naturally occurring examples

特性: Characterized by mean & standard deviation

confidence intervals – range likely contain unknown value & confidence level that value lies within range

Empirical rule 经验法则

1) 68% of data within 1 standard deviation of mean

2) 95% 2 sd

3)99.7% 3 sd

民意调查如何获知标准差?Standard error 少数人调查推断多数人

p = % sampled, n = sample size

SE = ((p*(100-p)/n))**0.5    //**表示幂

 



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