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# 機率

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### http:!//www.math.ntu.edu.tw/~hchu/Calculus/

⾃⾏閱讀Chapter 1,2,3,5。

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3Blue1Brown:

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⽤機率的語⾔去描述不確定性

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### 均勻分配

Uniform Distribution

https:!//en.wikipedia.org/wiki/Discrete_uniform_distribution

https:!//en.wikipedia.org/wiki/Uniform_distribution_(continuous)

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### ⼆項式分配

Binomial Distribution

https:!//en.wikipedia.org/wiki/Binomial_distribution

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### 常態分配

Normal Distribution

⼜稱⾼斯分配 (Gauss Distribution)

https:!//en.wikipedia.org/wiki/Normal_distribution

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### Z ∼ N(0, 1)

Z是⼀個隨機變數，遵守⼀個標準常態分配。

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### 機率論

Probability Theory

https:!//en.wikipedia.org/wiki/Probability_axioms

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H

T

H T H T H T

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H

T

H

T

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Random Variable

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skewness

kurtosis

### = E[ Z4 ]

Moment

https:!//en.wikipedia.org/wiki/Skewness

https:!//en.wikipedia.org/wiki/Kurtosis

https:!//en.wikipedia.org/wiki/Central_moment

https://en.wikipedia.org/wiki/Skewness#/media/

File:Relationship_between_mean_and_median_under_diﬀerent_skewness.png

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## 抽樣

Sampling

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### 從⺟體隨機抽取樣本

Population Sample

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https://zh.wikipedia.org/wiki/%E6%8A%BD%E6%A8%A3#/media/File:Simple_random_sampling.PNG

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### 台灣加權指數歷史收盤價 (未還原)

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https:!//en.wikipedia.org/wiki/Sortino_ratio https:!//en.wikipedia.org/wiki/Sharpe_ratio

https:!//en.wikipedia.org/wiki/

Compound_annual_growth_rate

https:!//breakingdownfinance.com/

finance-topics/performance- measurement/calmar-ratio/

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### 是否為常態分佈？

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Hypothesis Testing

## 檢定

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### •

Shapiro-Wilk test

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Anderson-Darling test

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Kolmogorov-Smirnov test

Jarque-Bera test

Pearson’s test

### χ2

https:!//en.wikipedia.org/wiki/Shapiro-Wilk_test

https:!//en.wikipedia.org/wiki/Anderson-Darling_test

https:!//en.wikipedia.org/wiki/Kolmogorov-Smirnov_test

https:!//en.wikipedia.org/wiki/Jarque-Bera_test

https:!//en.wikipedia.org/wiki/Pearson-_chi-squared_test

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Null Hypothesis

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## 對立假設

Alternative Hypothesis

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Statistic

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## 顯著性

Statistical Significance

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Type I Error

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## 型⼆誤差

Type II Error

https:!//en.wikipedia.org/wiki/Type_III_error

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## 型三誤差

Type III Error

https:!//en.wikipedia.org/wiki/Type_III_error

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### Bayes

https:!//en.wikipedia.org/wiki/Bayes'_theorem

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### ⽂⽒圖

https:!//en.wikipedia.org/wiki/Venn_diagram

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### = P(B | A) P(A)

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https://en.wikipedia.org/wiki/Bayes%27_theorem#A_more_complicated_example

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### 凱利賭徒

https:!//en.wikipedia.org/wiki/Kelly_criterion

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### 平賭

https:!//en.wikipedia.org/wiki/Martingale_(probability_theory)

### Martingale

https:!//rich01.com/blog-pos-22/

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### 反平賭

This communicative activity will give students a chance to orally practice the language targets of the unit before moving on to the main listening activities of the unit.. 4 l

This communicative activity will give students a chance to orally practice the language targets of the unit before moving on to the main listening activities of the unit.... l

This communicative activity will give students a chance to orally practice the language targets of the unit before moving on to the main listening activities of the unit.. 4 l

This communicative activity will give students a chance to orally practice the language targets of the unit before moving on to the main listening activities of the unit.. 4 l

This communicative activity will give students a chance to orally practice the language targets of the unit before moving on to the main listening activities of the unit.. 4 l

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