확률변수,RV (rev. 1.4)
Definition of RV ¶
A RV $\displaystyle X$ is a real-valued function of the experimental outcome.
$\displaystyle X:\mathbb{\Omega}\to\mathbb{R}$
여기서
Discrete RV (DRV) ¶
A RV $\displaystyle X$ is discrete if its range is finite or countably infinite.
여기서, range $\displaystyle r(X)=\left{x\middle|\exists\omega\in\mathbb{\Omega}\textrm{ such that }X(\omega)=x\right}$
X = # of heads
Ω = {HH, HT, TH, TT}
X(HH) = 2
X(TT) = 0
r(X) = {0, 1, 2}
여기서, range $\displaystyle r(X)=\left{x\middle|\exists\omega\in\mathbb{\Omega}\textrm{ such that }X(\omega)=x\right}$
즉 sample $\displaystyle \omega$ 를 $\displaystyle x$ 라는 값으로 대응시키는?
ex. two fair coin tosses그런 함수가 $\displaystyle X$ 이고 그것을 독립변수(or 정의역)로 하는 대응관계가 range r? 조건제시법 이해가 잘...
X = # of heads
Ω = {HH, HT, TH, TT}
X(HH) = 2
X(TT) = 0
r(X) = {0, 1, 2}
ex. sampling a number ω from ［-1,1］
$\displaystyle X(\omega)=\begin{cases}1,&\textrm{ if }\omega>0\\0,&\textrm{ if }\omega=0\\-1,&\textrm{ if }\omega<0\end{cases}$
$\displaystyle X(\omega)=\begin{cases}1,&\textrm{ if }\omega>0\\0,&\textrm{ if }\omega=0\\-1,&\textrm{ if }\omega<0\end{cases}$
페이지: 이산확률변수,discrete_RV
Probability mass function (PMF) ¶
The PMF $\displaystyle p_X(x)$ of a DRV $\displaystyle X$ is defined as:
$\displaystyle p_X(x)=$
$\displaystyle p_X(x)=P(X=x)=P\left(\left{\omega\in\mathbb{\Omega}\middle|X(\omega)=x\right}\right)$
위의 동전던지기를 예로 들면$\displaystyle p_X(x)=$
¼ if x=0 TT
½ if x=1 HT TH
¼ if x=2 HH
½ if x=1 HT TH
¼ if x=2 HH
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