Conditional Probability and the Independence of Trial

Conditional Probability is defined as below. It implies that probability space should be restricted in A to get  . It can be shown as like a picture below. Let’s consider the independence of events. If we assume that there are 10 balls in a box. (# of black balls  = 7, # of red balls …

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Joint Probability and Chain Rule

1. Joint Probability Function Joint probability can be classified with discrete random variables and continuous random variables. In this post I want deal with just discrete random variables and its joint probability function. Let is given by   The function   will be referred to as the joint probability function. [referred by Mathematical Statistics with …

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Conditional Independence

Let’s consider conditional independence. I would recommend an example below which is the one of the best example to explain conditional independence intuitively. I’ve heard an on-line machine learning lecture from Prof. Il-Chul Moon who is the professor at KAIST. I would like to quote an picture from that lecture (3.2) There is an commander who …

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