63 lines
1.1 KiB
Markdown
63 lines
1.1 KiB
Markdown
---
|
||
title: 隨機變數 (Random Variable)
|
||
description:
|
||
published: true
|
||
date: 2025-12-28T19:20:34.516Z
|
||
tags:
|
||
editor: markdown
|
||
dateCreated: 2025-12-28T16:41:51.938Z
|
||
---
|
||
|
||
## Discrete
|
||
|
||
### Probability Mass Function (PMF)
|
||
|
||
A set of probability value **p~i~** assigned to each of the values taken by the discrete random variables **x~i~**.
|
||
|
||
**0 ≤ p~i~ ≤ 1 and ∑ p~i~ = 1**
|
||
|
||
Probability
|
||
$\leq$
|
||
|
||
Expectation
|
||
|
||
|
||
### Cumulative Distribution Function (CDF)
|
||
|
||
|
||
|
||
|
||
## Continuous
|
||
|
||
### Probability Density Function (PDF)
|
||
|
||
Probabilistic properties of a continuous random variable.
|
||
|
||
Expectation
|
||
|
||
|
||
### Cumulative Distribution Function (CDF)
|
||
|
||
|
||
|
||
|
||
|
||
|
||
### Symmetric
|
||
|
||
If there is a point that,
|
||
|
||
Then,
|
||
|
||
Is the expectation of this random variable, equal to the point of symmetry.
|
||
|
||
### Median and Quantiles
|
||
|
||
The middle value of the random variable.
|
||
For median, set p to 0.5.
|
||
|
||
|
||
### Variance
|
||
|
||
A positive quantity that measures the spread of the distribution of the random variable about its mean value.
|
||
Larger values of the variance indicate that the distribution is more spread out. |