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# System prepended metadata

title: 機率CH6 - Continuous Random Variables

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# 機率CH6 - Continuous Random Variables
## 6.1&emsp; Probability Density Functions
## Motivation
- [ ] read
往上跳的高度就是機率的高度
想要從離散的情況討論到連續的情況
![](https://i.imgur.com/KR3Vc7b.png)
## Definition of Density Functions
- [ ] read
![](https://i.imgur.com/Pp9p5Az.png)
## Property
- [ ] read
![](https://i.imgur.com/6snhMAV.png)
![](https://i.imgur.com/zuSkvaD.png)
![](https://i.imgur.com/G6LFV1y.png)
![](https://i.imgur.com/znS1nI1.png)
![](https://i.imgur.com/S0rju9n.png)
![](https://i.imgur.com/4D70Ti3.png)
## 6.2&emsp;Density Function of a Function of a Random Variable
## density function of random variables
- [ ] read
![](https://i.imgur.com/UVoYfK5.png)
![](https://i.imgur.com/0CDWeai.png)
## 反函數
- [ ] read
![](https://i.imgur.com/gdNNchy.png)
具有反函數 <=> 嚴格遞增或嚴格遞減
## methods of transformation
- [ ] read
![](https://i.imgur.com/YffXjnz.png)
![](https://i.imgur.com/Ks6pcG1.png)
![](https://i.imgur.com/39rpoaB.png)
## 6.3&emsp;Expectations and Variances
## Definition of Expectations of Continuous Random Variables
- [ ] read
![](https://i.imgur.com/K9LWBUT.png)
## Remark6.2
- [ ] read
![](https://i.imgur.com/qODFJgI.png)
## Cauchy Random Variable
- [ ] read
期望值不存在
![](https://i.imgur.com/uySUFsv.png)
![](https://i.imgur.com/2b6WjtQ.png)
## Remark6.4
- [ ] read
![](https://i.imgur.com/FzS1ary.png)
## The Law of Unconscious Statistician
- [ ] read
![](https://i.imgur.com/SC3Jsy1.png)
![](https://i.imgur.com/01Ua4W5.png)
![](https://i.imgur.com/ekDm3Ch.png)
## Col6.2
- [ ] read
![](https://i.imgur.com/Obf4AfK.png)
## Definition of Variances of Continuous Random Variables
- [ ] read
![](https://i.imgur.com/mBQetzP.png)
## Remark6.6
- [ ] read
![](https://i.imgur.com/95zLlO6.png)

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