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title: 機率TP5
---
# Theory of Probability：<br>Discrete Random Variables- Basics
NTNU 機率論

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###### tags: `NTNU` `CSIE` `必修` `Theory of Probability`

## Table of Contents
[TOC]

## The Notion and Definition of Random Variables
### Notion of Random Variables 隨機變數的概念
### Definition of Random Variables 隨機變數的定義
- 給定一個實驗與可能結果的對應集合，隨機變量將特定數字與每個結果相關聯<!-- Given an experiment and the corresponding set of possible outcomes( the sample space), a random variable associates a particular number with each outcome -->
- This number is referred to as the (numerical) value of the random variable
- We can say a random variable is a real-valued function of the experimental
### Main Concepts Related to Random Variables
- For a probabilistic model of an experiment
- A random variable is a real-valued function of the outcome of the experiment
- A function of a random variable defines another random variable
- We can associate with each random variable certain “averages” of interest such the mean and the variance
- A random variable can be conditioned on an event or on another random variable
- There is a notion of independence of a random variable from an event or from another random variable
### Discrete/Continuous Random Variables

## Probability Mass Function (PMF)
## Some Commonly-used Discrete Random Variables
## Functions of Random Variables