NiKoNiKoNiUI
Home
Archive
My
Anime
Notes
Albums
About
About Me
Friends
Others
Projects
Skills
Timeline
Home
Archive
My
Anime
Notes
Albums
About
About Me
Friends
Others
Projects
Skills
Timeline
The fallen leaves tell a story
NiKoNiKoNi
GitHub
Announcement
Welcome to my blog! I will share my study notes and technical articles here.
Tags
analysis
Blogging
Demo
Example
Markdown
math
Mermaid
mizuki
notes
probability theory
Video
Categories
Analysis
12
Examples
4
Probability Theory
19
Site Statistics
Posts
35
Categories
3
Tags
11
Total Words
23,032
Running Time
0
days
Last Activity
0
days ago
Sun
Mon
Tue
Wed
Thu
Fri
Sat
93 words
1 minute
2.3 随机变量的函数
2025-11-26
Probability Theory
/
math
/
probability theory
/
notes
2.3 随机变量的函数
#
随机变量函数的定义
#
设
Y
=
g
(
X
)
Y = g(X)
Y
=
g
(
X
)
，其中
g
g
g
是实值函数
Y
Y
Y
也是一个随机变量
函数分布列的计算
#
一般公式
：
p
Y
(
y
)
=
∑
{
x
∣
g
(
x
)
=
y
}
p
X
(
x
)
p_Y(y) = \sum_{\{x|g(x)=y\}} p_X(x)
p
Y
(
y
)
=
∑
{
x
∣
g
(
x
)
=
y
}
p
X
(
x
)
特殊情况
：
Y
=
∣
X
∣
Y = |X|
Y
=
∣
X
∣
，
Z
=
X
2
Z = X^2
Z
=
X
2
等
期望规则
#
基本公式
：
E
[
g
(
X
)
]
=
∑
x
g
(
x
)
p
X
(
x
)
E[g(X)] = \sum\limits_{x} g(x)p_X(x)
E
[
g
(
X
)]
=
x
∑
g
(
x
)
p
X
(
x
)
验证
：通过
Y
=
g
(
X
)
Y = g(X)
Y
=
g
(
X
)
的分布列定义推导得出
2.3 随机变量的函数
https://miku.nikonikoni.blog/posts/propability_theory/2-3-function-of-random-variable/
Author
nikonikoni
Published at
2025-11-26
License
Unlicensed
Some information may be outdated
2.2 分布列
2.4 期望、均值和方差
Sample Song
Sample Artist
Sample Song
Sample Artist
0:00 / 0:00
