---
title: 202109 MathStat
tags: teach:MS
---
# 202109 Math Stat

:::success
This handout is prepared by Prof. [Huei-Wen Teng](https://hackmd.io/cxnJOabrRQaLDY7w68_3MA) for the fall semester, 2021. Previously offered in Falls of 2017, 2018, 2019, 2020.
:::

## Links

| Type| Description |
|---|---|
| Link| [助教 Office Hours] 星期一三 19:00~21:00 |
| Vedio| [已整理](https://drive.google.com/drive/folders/1kPg9SKbdOLuUjZVZeSY_FaHZXDvALszM?usp=sharing), [未整理](https://drive.google.com/drive/folders/16Y6XGv6dr6Hs1-vWTCyLOmiygXtla_4Q?usp=sharing) |
| Jambaord| [一開始](https://jamboard.google.com/d/1qxeSneMmztobYDJN3XjVW6wqnLnYdmWl1HwS2fHmuIg/viewer?f=2), [10/26](https://jamboard.google.com/d/1AENO2v9d1Uh7MLluvipPSByL5Hvi8P0MqxF0kzM7k2o/viewer?f=1), [11/6](https://jamboard.google.com/d/12zx_pUJ0NBTBHzfrHX_WFZfqEnZQPYZiWsDhAVElZzE/viewer?f=0)

Unless otherwise specified, we will follow the following table for the schedule and homework assignments throughout this semester.

## Part I: 同步線上課程

| No | Date | Topic | Hw | Assignment |
|---|---|-----|---|-----|
| 1 | 9/14 | Chapter 1 | H1 | C1: 1, 6, 15, 21, 25, 27, 33 |
| | | Ch1. Probabiliy |
| 2 | 9/21 | No class (中秋節) | | |
| 3 | 9/28 | C1. Conditional probabilities, independence, discrete RV | H2 | C1: 36, 37, 47, 49, 50, 55, 64, 74, 77 |
| 4 | 10/5 | [Chapter 2](https://hackmd.io/6Z7hQyNwSy62W32x_rAl5Q) | H3 | C2: 1, 3, 6, 7, 10, 21, 26, 31, 35, 40. |
| | | C2. Discrete RV, continuous RV | | |
| 5 | 10/12 | C2. Function of random variables | H4 | C2: 45, 48, 49, 51, 53, 54, 55, |
| 6 | 10/19 | [Chapter 3](https://hackmd.io/bmFwN0Y-Rv21LXJl2XJHVw) | H5 |C2: 59, 60, 64, 67, 72. |
| | | C3. Joint and conditional distributions. | | C3: 1, 3, 7, 9. |
| 7 | 10/26 | C3. Bayesian inference, sum and quotions, general cases | H6 |C3: 12, 13, 16, 17, 18, 27, 35, 43, 46, 47, 48, 51, 52. |
| 8 | 11/2 | [Chapter 4](https://hackmd.io/34LcoFlYQseLzOnrI0aC9w?both) | H7 (不用交) | C3.6: 59, 62, 64|
|||C4.1. The expected value of a random variable||C3.7: 77, 79|
| | | | | C4.1: 6 (a-c), 18, 19, 25, 31 |
| | | | | Reading: Examples A, B, C, E, F, G |
| 9 | 11/9 | [Exam 1](https://hackmd.io/ZVxLV13zQMOgtlLfvf3__g)||
| 10 | 11/16 | 自主學習 | |
||11/19| 13:20-16:20 office hours, M415|
|11|11/23| [元宇宙未來領袖訓練營](https://hackmd.io/bepJtfQ0Rg6tI94_p6p5Xw) |

## Part II: 實體授課 M102

|Week|Date |Description| Homework|
|---|---|---|---|
| 12 | 11/30 |[Chapter 4](https://hackmd.io/34LcoFlYQseLzOnrI0aC9w?both) |Hw8.
||| C4.2. Covariance and stadard deviation| C4.2: 42, 43.
||| C4.3. Covariance and correlation| C4.3: 48, 52*, 54
|13|12/7||Hw9.|
||| C4.4. Conditional Expectations and predictions| C4.4: 63, 64.
||| C4.5. Moment generating functions | C4.5: 79, 80, 85, 89
|14|12/14 |[Chapter 5](https://hackmd.io/WLYNYR7yS6mW-bXMmSzFfg). Law of large numbers and central limit theorem |Hw 10.
|||5.1: Introduction | C5. 19, 23.
|||5.2: The Law of Large Numbers| C5. 13, 16, 17, 18, 30.
|||5.3: Convergence in Distribution and the Central Limit Theorem|
|15 | 21 | [Chapter 6](https://hackmd.io/UNousWNbShqqsLCFsD0Vqw). Distributions derived from normal distributions |Hw 11. (不用交) |
|||6.1 Introduction|C6: 3, 5, 6, 11. |
|||6.2 $\chi^2$, $t$, and $F$ distribution|
|||6.3 The sample mean and the sample variance|
|15|12/21|[Chapter 8](https://hackmd.io/arG3RluISY-tGsDC1TlELw). Estimation of parameters and fitting of probability distributions| C8: 4abc, 5abc, 7ab, 20, 54, 57a.
|||8.4 The method of moments|
|||8.5 The method of maximum likelihood|
| 16 | 12/28 | Exam 2 | | |
| 17 | 1/4 | Discussions (by appointment) | | |
| 18 | 1/11 | Discussions (by appointments) | | |

<!--|||8.1 Introudction |
|||8.2 Fitting the poisson distribution to Emissions of alpha particles|
|||8.3 Parameters estimation|
|||8.6 The Bayesian approach to parameter estimation -
|||8.7 Efficiency and the Cramer-Rao lower bound|
|||8.8 Sufficiency|
->

### Further topics

Due to time limits, we will not cover the following.

||| Chapters|
|--|---|---|
|||9. Hypothesis testing. H13|C9: 1, 3, 4, 5, 7, 9, 23, 26|

### emoji

|Emoji| Description|
|---|---|
|:apple:| great to know
| :construction: | under construction|