# 統計學一 Statistics
PPT筆記
[toc]
## [目錄 提供關鍵字方便查找](https://hackmd.io/@RuH9UULLRMuRo2iEsweIqA/rk58C9PXkl)
## [Week 1 What is Statistics? 待補 未完成修訂](https://hackmd.io/@RuH9UULLRMuRo2iEsweIqA/HJI01MHGJg)
population (母體)
* A sample (樣本)
* Descriptive statistics (敘述統計)
* Inferential statistics (推論統計)
* parameter (母數) :
* statistic (統計量):
levels of data measurement (資料測量尺度, 資料尺度)
* nominal scale (名目尺度)
* ordinal scale (次序尺度)
* interval scale (區間尺度)
## [Week 2 Graphical Descriptive Techniques 待補 未完成修訂](https://hackmd.io/@RuH9UULLRMuRo2iEsweIqA/HJAcefBG1l)
frequency distribution = frequency tables
* class midpoint = class mark
* relative frequency
* cumulative frequency
Visualizing quantitative data.
* histogram
* right-tailed = positively skewed = right-skewed
* left-tailed = left-skewed = negatively skewed
* symmetric
* bimodal 雙峰
* extreme values 、 outliers.
* frequency polygon
* Ogives
* Stem-and-leaf plots
* Visualizing qualitative data.
* Pie charts 圓餅圖
* Bar charts
* Pareto charts
Visualizing time-series data.
* Cross-sectional data
* Time-series data
Visualizing two variables
* Cross tabulation 列聯表 樞紐分析表
* contingency table
* Scatter plots : 兩者都是量化資料的
## [Week 3 Numerical Descriptive Techniques 待補 未完成修訂](https://hackmd.io/@RuH9UULLRMuRo2iEsweIqA/SkRfbfBzyx)
Measures of central tendency. 集中趨勢測度
* Medians 中位數
* Means
* Modes
Measures of variability.
* variability.
* Chebyshev’s theorem
* Law of large numbers
* Quartiles
* Percentiles
* Standard scores = z score = z value
* Moments 動差
* Skewness 偏態
* Kurtosis 峰態
* Covariances 共變數
correlation coefficient 相關係數
* 1. 變異係數的定義
* 2. 計算變異係數的程式碼
* 3. 變異係數的意義
* 範例輸出
sample covariance
* sample correlation coefficient
## [week 4 Basics of Probability and Random Variables待補 未完成修訂](https://hackmd.io/@RuH9UULLRMuRo2iEsweIqA/BkNtWfSMJg)
Probability
* collectively exhaustive 互斥 \(Pr(X ∩ Y ) = 0\) 與 collectively exhaustive詳盡的
* Complements
* The mn counting rule乘法計數法則 - 發生在 兩者為獨立事件時
* Sampling with replacement. 取後有放回
* Sampling without replacement (combinations). 不放回抽樣（組合）。
* 當樣本數 n相對於總體數 N很小時， 取後不放回的過程可以用取後放回的近似來處理 => \(N^n\)
* Joint probability tables 列聯機率表
* Independent events 獨立事件
* Bayes’ theorem.
* Belief updating
* 步驟：
* Bayesian updating or Bayesian inference.
Random Variables
* Discrete random variables
* Continuous random variables
* Describing a discrete distribution
* Probability mass functions 機率質量函數 PMF => discrete RV
* Linear functions of a random variable
* Expectation of a sum of RVs
* Variance of sum of RVs
## [Week 5 Well-known Discrete Probability Distributions 待補 未完成修訂](https://hackmd.io/@RuH9UULLRMuRo2iEsweIqA/By_eMMHzyl)
Discrete Probability Distributions
* Bernoulli distributions.
* Geometric distributions.
* Binomial distributions.
* Hypergeometric distributions.
* Poisson distribution
## [Week 6 (Well-known) Continuous Probability Distributions 待補 未完成修訂](https://hackmd.io/@RuH9UULLRMuRo2iEsweIqA/HJi5QMrMJe)
Continuous Probability Distributions
* Continuous random variables
* Probability density functions
* Cumulative distribution functions
* Uniform distributions \(X ∼ Uni(a, b)\) => \(f(x) = c\)
* Exponential distributions 指數分佈 \(X ∼ Exp(λ)\)
* Newsvendor model
* newsvendor quantity
* M/M/1 queue.
* expected system size \(L\) in the long run
## [Week 7 The Normal Distribution 待補 未完成修訂](https://hackmd.io/@RuH9UULLRMuRo2iEsweIqA/BkMW4MHz1l)
* The Normal Distribution = Gaussian distributions.
* Standard normal distributions = z distribution.
* 用 binomial 近似 normal
* Sample means
* Chebyshev's Theorem:
## Week 8 Midterm
未訂正 待補 只考了45分 我該停修了
## [Week 9 Chapter 5: Data Collection and Sampling](https://hackmd.io/@RuH9UULLRMuRo2iEsweIqA/Hk89EfHM1g)
## [Week 10 Chapter 9: Sampling Distributions](https://hackmd.io/@RuH9UULLRMuRo2iEsweIqA/rJATvJaW1e)
## [Week 11 Chapter 10: Introduction to Estimation](https://hackmd.io/@RuH9UULLRMuRo2iEsweIqA/SJf5qzBMJl)
## [Week 12 Chapter 11: Introduction to Hypothesis Testing ](https://hackmd.io/@RuH9UULLRMuRo2iEsweIqA/SkvwO8Lfyl)
## [Week 13,14 Chapter 12: Inference about a Population](https://hackmd.io/@RuH9UULLRMuRo2iEsweIqA/BJjnTcPXkg)
## Final 2023
# [GitHub 作業檔案連結](https://github.com/LEE-CHIEN-AN/Statistics)
# 統計學一下 Statistics II
## [Week 1 Chapter 13: Inference about Comparing Two Populations](https://hackmd.io/@RuH9UULLRMuRo2iEsweIqA/ryEdIsN9Jg)
## [Week 2 Chapter 13 Inference about Comparing Two Populations](https://hackmd.io/@RuH9UULLRMuRo2iEsweIqA/B1sLVkGsJg)
## [Week 3 Chapter 14: Analysis of Variance (ANOVA) Part A](https://hackmd.io/@RuH9UULLRMuRo2iEsweIqA/ryfKwH3s1e)
## [Week 4 Chapter 14 Analysis of Variance Part B](https://hackmd.io/@RuH9UULLRMuRo2iEsweIqA/HywdUCfnJx)
## [Week 5 Chapter 15: Chi-Squared Tests](https://hackmd.io/@RuH9UULLRMuRo2iEsweIqA/r1eXCJu31x)
## [Week 6 Chapter 19 Nonparametric Methods ](https://hackmd.io/@RuH9UULLRMuRo2iEsweIqA/Hkl65km-pyx)
## [Week 7 Chapter 19 Nonparametric Methods Part B: whether the population locations differ](https://hackmd.io/@RuH9UULLRMuRo2iEsweIqA/SyN_hdGRyl)
## [Week 9 Linear Regression (Part 1)](https://hackmd.io/@RuH9UULLRMuRo2iEsweIqA/ryzvEnCRyl)
## [Week 10 Linear Regression (Part 2)](https://hackmd.io/@RuH9UULLRMuRo2iEsweIqA/S1TdiILJxg)
## [Week 11 Linear Regression (Part 3)](https://hackmd.io/@RuH9UULLRMuRo2iEsweIqA/HJZ2TSeeee)
## [Week 12 Logistic Regression](https://hackmd.io/@RuH9UULLRMuRo2iEsweIqA/HJUh3Kdlxe)
## [Week 12 Predictive Linear Regression](https://hackmd.io/@RuH9UULLRMuRo2iEsweIqA/rJqejXeWge)
## [Week 13 Time－Series Analysis（Part 1）](https://hackmd.io/@RuH9UULLRMuRo2iEsweIqA/HJjYkPN-xl)
## [Week 14 Time-Series Analysis (Part 2)](https://hackmd.io/yI4Nn3iBTbuWRjhkB076Iw?view)
## [Week 15 Final project ppt](https://www.canva.com/design/DAGoSJpDAvc/64yh_HxriaGOiGeskyEqfA/view?utm_content=DAGoSJpDAvc&utm_campaign=designshare&utm_medium=link2&utm_source=uniquelinks&utlId=h653df963c0)
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