機率
===
- [機率](/lB9C4si-SSO30PpinQB_DA)
### 課程資訊 Information
- 授課教師 Lecturer：謝秉均
- 授課時間 Semester：112-1, 2023 Fall
- 評分方式 Grading：
- Homeworks: 40% (including written and programming tasks)
- HW1: Axioms, Sets, and Conditional Probability
- HW2: Independence, Combinatorics, and RVs
- HW3: Continuous RV and Joint Distributions
- HW4: Concentration Inequalities, LLN, and Multivariate Normal
- Midterm: 30%
- Final Exam: 30%
- [課程綱要 Syllabus](https://timetable.nycu.edu.tw/?r=main/crsoutline&Acy=112&Sem=1&CrsNo=515512&lang=zh-tw)
### 上課筆記 Notes
- [機率 - 1 (Set Thm ~ Entropy)](/oKa988LySACLrk_HfyUxTw)
- [機率 - 2 (Expectation ~ Conti R.V.)](/KKBQgYdCSAqJvHYDUbZ94w)
- [機率 - 3 (Normal R.V. ~ Conditional Distribution)](/CNC_a3uyRXCDTkNrqer00g)
- [機率 - 4 (Bivariate Normal R.V. ~ ?)](/JLIJnqUkSpyAoZ18mfwxig)

### Cheatsheet
#### 期中
- [x] PMF of Poisson R.V.
- [x] prop of a valid CDF
* $F_X(t)$ is non-decreasing
* $\displaystyle\lim_{t\to\infty}F_X(t)=1$, $\displaystyle\lim_{t\to-\infty}F_X(t)=0$
* $F_X(t)$ is right-continuous ($F_X(t^{+})=F_X(t)$)
- [x] Borel-Cantelli Lemma
#### 期末
- [x] normal r.v.
- PDF
- [x] joint & marginal 的轉換
- [x] MGF
- 各種 r.v. 的 MGF
- [x] property of expectation of 2 R.V.
- [x] Bivariate Normal R.V.
- joint PDF
- Property
- [x] Covariance, Correlation Coefficient
- [x] Concentration inequality
- [ ] LLN
- Convergence in probability
- Convergence almost Surely
- [ ] Central Limit Theorem
- Convergence in distribution
- [ ] Martingale
- Azuma’s Inequality