Basic probability theory - 편집 역사

2020년 11월 16일 (월) 12:26에 Pythagoras0님의 편집

2020-11-16T12:26:35Z

2020년 11월 13일 (금) 07:14에 imported>Pythagoras0님의 편집

2020-11-13T07:14:43Z

imported>Pythagoras0: 새 문서: ==introduction== * Let $(\Omega, \mathcal{F}, P)$ be probability space * A real-valued function $X : \Omega\to \mathbb{R}$ is called a random variable * let $A\subseteq \mathbb{R}$ be...

2016-06-09T03:03:06Z

새 문서: ==introduction== * Let $(\Omega, \mathcal{F}, P)$ be probability space * A real-valued function $X : \Omega\to \mathbb{R}$ is called a random variable * let $A\subseteq \mathbb{R}$ be...

새 문서

==introduction==
* Let $(\Omega, \mathcal{F}, P)$ be probability space
* A real-valued function $X : \Omega\to \mathbb{R}$ is called a random variable
* let $A\subseteq \mathbb{R}$ be the range of $X$, $A=\{s|X(s)=x,s\in S\}$. We call $A$ the space of $X$
* $\{X=x\}$ denote the subset $\{s|X(s)=x\}$ of $\mathbb{R}$
* the induced probability measure $P_X : \mathbb{R}\to [0,1]$
* probability density function $f : \mathbb{R}\to [0,\infty)$ of $X$ satisfies
$$
P_{X}(X\in A)=\int_A f(x)\, dx=1
$$
and
$$
P_{X}(X\in B)=\int_B f(x)\, dx
$$
for $B\subseteq A$.

[[분류:Probability]]

← 이전 판		2020년 11월 13일 (금) 07:14 판
17번째 줄:		17번째 줄:

	[[분류:Probability]]		[[분류:Probability]]
		+	[[분류:migrate]]

@@ 1번째 줄: / 1번째 줄: @@
 ==introduction==
-* Let $(\Omega, \mathcal{F}, P)$ be probability space
+* Let <math>(\Omega, \mathcal{F}, P)</math> be probability space
-* A real-valued function $X : \Omega\to \mathbb{R}$ is called a random variable
+* A real-valued function <math>X : \Omega\to \mathbb{R}</math> is called a random variable
-* let $A\subseteq \mathbb{R}$ be the range of $X$, $A=\{s|X(s)=x,s\in S\}$. We call $A$ the space of $X$
+* let <math>A\subseteq \mathbb{R}</math> be the range of <math>X</math>, <math>A=\{s|X(s)=x,s\in S\}</math>. We call <math>A</math> the space of <math>X</math>
-* $\{X=x\}$ denote the subset $\{s|X(s)=x\}$ of $\mathbb{R}$
+* <math>\{X=x\}</math> denote the subset <math>\{s|X(s)=x\}</math> of <math>\mathbb{R}</math>
-* the induced probability measure $P_X : \mathbb{R}\to [0,1]$
+* the induced probability measure <math>P_X : \mathbb{R}\to [0,1]</math>
-* probability density function $f : \mathbb{R}\to [0,\infty)$ of $X$ satisfies
+* probability density function <math>f : \mathbb{R}\to [0,\infty)</math> of <math>X</math> satisfies
-$$
+:<math>
 P_{X}(X\in A)=\int_A f(x)\, dx=1
-$$
+</math>
 and
-$$
+:<math>
 P_{X}(X\in B)=\int_B f(x)\, dx
-$$
+</math>
-for $B\subseteq A$.
+for <math>B\subseteq A</math>.
 [[분류:Probability]]
 [[분류:migrate]]