"Basic probability theory"의 두 판 사이의 차이

2020년 11월 16일 (월) 05:26 기준 최신판

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 \(B\subseteq A\).

@@ 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]]