Pattern Recognition - Chapter 1: Basic probability theory
1. Discrete - Continuous random variable
1.1. Discrete random variable
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1.2. Continuous random variable
![](https://static.wixstatic.com/media/64c52b_543e09aeb43d45c8a3750fc342c10c41~mv2.png/v1/fill/w_320,h_194,al_c,q_85,enc_auto/64c52b_543e09aeb43d45c8a3750fc342c10c41~mv2.png)
![](https://static.wixstatic.com/media/64c52b_9386bb1b3bd144cba14d6a90654fcb25~mv2.png/v1/fill/w_200,h_62,al_c,q_85,enc_auto/64c52b_9386bb1b3bd144cba14d6a90654fcb25~mv2.png)
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2. Statistical independence
2.1. Marginal distribution
![](https://static.wixstatic.com/media/64c52b_698b9549084a42f388a2317dcd408c50~mv2.png/v1/fill/w_188,h_64,al_c,q_85,enc_auto/64c52b_698b9549084a42f388a2317dcd408c50~mv2.png)
![](https://static.wixstatic.com/media/64c52b_156890f0564c40169f3eafa38f65e7c6~mv2.png/v1/fill/w_320,h_220,al_c,q_85,enc_auto/64c52b_156890f0564c40169f3eafa38f65e7c6~mv2.png)
2.2. Statistical independence
![](https://static.wixstatic.com/media/64c52b_cd17bfa3f887495ea01ef331a8840d20~mv2.png/v1/fill/w_320,h_220,al_c,q_85,enc_auto/64c52b_cd17bfa3f887495ea01ef331a8840d20~mv2.png)
2.3. Covariance
![](https://static.wixstatic.com/media/64c52b_ac4b0394a6544fa787ff86c621e21867~mv2.png/v1/fill/w_620,h_178,al_c,q_85,enc_auto/64c52b_ac4b0394a6544fa787ff86c621e21867~mv2.png)
![](https://static.wixstatic.com/media/64c52b_cf295cb170e74e55b9a918e558b47bd5~mv2.png/v1/fill/w_200,h_102,al_c,q_85,enc_auto/64c52b_cf295cb170e74e55b9a918e558b47bd5~mv2.png)
![](https://static.wixstatic.com/media/64c52b_964517a8de20467e8cf341d6a51df47e~mv2.jpg/v1/fill/w_400,h_269,al_c,q_80,enc_auto/64c52b_964517a8de20467e8cf341d6a51df47e~mv2.jpg)
(*Source: Rudolf Kruse et al. Texts in Computer Science)
![](https://static.wixstatic.com/media/64c52b_8f35c792096e4fcab4656224f90c10e6~mv2.png/v1/fill/w_320,h_144,al_c,q_85,enc_auto/64c52b_8f35c792096e4fcab4656224f90c10e6~mv2.png)
(*Source: https://en.wikipedia.org/wiki/Correlation_and_dependence)
3. Conditional probability
3.1. Conditional probability
![](https://static.wixstatic.com/media/64c52b_125b908304034f4b9c944926826240f8~mv2.png/v1/fill/w_141,h_53,al_c,q_85,enc_auto/64c52b_125b908304034f4b9c944926826240f8~mv2.png)
3.2. Bayes rule
![](https://static.wixstatic.com/media/64c52b_46b06fc0d1a34244bdcdfc0770a05f74~mv2.png/v1/fill/w_129,h_61,al_c,q_85,enc_auto/64c52b_46b06fc0d1a34244bdcdfc0770a05f74~mv2.png)
![](https://static.wixstatic.com/media/64c52b_125b908304034f4b9c944926826240f8~mv2.png/v1/fill/w_141,h_53,al_c,q_85,enc_auto/64c52b_125b908304034f4b9c944926826240f8~mv2.png)
![](https://static.wixstatic.com/media/64c52b_1ca01711d2104015999cd6ed163dda00~mv2.png/v1/fill/w_234,h_72,al_c,q_85,enc_auto/64c52b_1ca01711d2104015999cd6ed163dda00~mv2.png)
![](https://static.wixstatic.com/media/64c52b_ea858f82524643d596a10228db014f67~mv2.png/v1/fill/w_465,h_52,al_c,q_85,enc_auto/64c52b_ea858f82524643d596a10228db014f67~mv2.png)
![](https://static.wixstatic.com/media/64c52b_df43b7a2f703423eb55e7363ff280a31~mv2.png/v1/fill/w_320,h_220,al_c,q_85,enc_auto/64c52b_df43b7a2f703423eb55e7363ff280a31~mv2.png)
![](https://static.wixstatic.com/media/64c52b_52b579319ae946d18a084af7e9e83c05~mv2.png/v1/fill/w_320,h_47,al_c,q_85,enc_auto/64c52b_52b579319ae946d18a084af7e9e83c05~mv2.png)
3.3. Naive Bayes rule