Week04. Statistics with R Part01

Coursera 2018.01

The Normal Distribution

1. Normal Distribution

• normal distribution

  

  $\sigma$ - standard deviation

• 68 - 95 - 99.7% rule

  

  3$\sigma$原则

  • practice

    

    

• standardizing with Z scores

  

  • standardized(Z) score

  • Z-score 的均值为0

  • 不寻常的observation $|Z| > 2$

• percentiles

  

  • percentile is the percentage of observations that fall below a given data point

  • computing percentiles - using R

    值为-1及以下的概率(percentiles)

    pnorm(-1, mean = 0, sd = 1)
    [1] 0.1586553

  • 当概率分布是正态分布时，Z-score和percentiles有一一的对应关系？(待考证)

  • practice

    

2. evaluating the normal distribution

• normal probability plot

  

• anatomy of a normal probability plot

  

• skewness

  

  • right skew的那个说明集中分布在左侧，左侧的概率要大些。

3. working with the normal distribution

嗯嗯，简单的例子

Binomial Distribution

1. binomial distribution

• the Milgram experiment

  测试参与测试的teacher会不会违背他们的自己的意愿去电击的比率。

  

• Bernouilli random variables

  • each person in Milgram's experiment can be thought of as a trial

  • a person is labeled a success if she refuses to administer a severe shock, and failure if she administers such shock

  • since only 35% of people refused to administer a shock, probability of success is p = 0.35.

  • when an individual trial has only two possible outcomes, it is called a Bernoulli random variable

    也称为伯努利实验。

• example

  

• binomial distribution

  the binomial distribution describes the probability of having exactly $k$ successes in $n$ independent Bernouilli trials with probability of success $p$

  

  

• binomial conditions

  

• excepted value and standard deviation

  

2. normal approximation to binomial

• 二项分布与正态分布的近似

  

  

  • 因为用正态分布拟合的方法算，忽略了等于70的情况，所以作0.5的调整，调整为69.5。这样最后的结果更接近真实的结果。

  • 二者能够近似的要求

    

    

3. working with the binomial distribution

• example

  

  

  • 1000个中选600个，根据大数定律，这个时候结果应当非常趋近560，偏离40个是比较大的偏离，发生的可能性很小。相对而言，10各中有6个比较容易发生。