# 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) ## h2 - [ ] read ## h2 - [ ] read ## h2 - [ ] read ## h2 - [ ] read ## h2 - [ ] read ## h2 - [ ] read ## h2 - [ ] read ## h2 - [ ] read ## h2 - [ ] read ## h2 - [ ] read ## h2 - [ ] read ## h2 - [ ] read ## h2 - [ ] read ## h2 - [ ] read ## h2 - [ ] read ## h2 - [ ] read ## h2 - [ ] read ## h2 - [ ] read ## h2 - [ ] read ## h2 - [ ] read ## h2 - [ ] read ## h2 - [ ] read ## h2 - [ ] read ## h2 - [ ] read ## h2 - [ ] read ## h2 - [ ] read ## h2 - [ ] read ## h2 - [ ] read ## h2 - [ ] read ## h2 - [ ] read ## h2 - [ ] read