Conditional probability mass function ¶

조건부 확률질량함수,conditional_pmf
조건부 기대치,conditional_expected_value
조건부 분산,conditional_variance

from http://www.kocw.net/home/search/kemView.do?kemId=1279832 8. Conditional Probability, Independence of Events, Sequential Experiments 1:02:39

Let d.r.v.(discrete random variable) X with pmf P_X and event C with P(C)>0.
→ the conditional probability mass function of X given event C:

$\displaystyle P_X(x|C)=P(X=x|C)=\frac{P(\{X=x\}\cap C)}{P(C)}$

def.
(a) the conditional expected value of X given event C:

$\displaystyle E(X|C)=m_{X|C}=\sum_{\textrm{all }k}x_kP_k(x_k|C)$

사건 C가 일어났을 때 X의 조건부 기대치.
pmf 자리에 조건부pmf가 왔음.

(b) the conditional variance of X given event C:

$\displaystyle VAR(X|C)=E\left((X-m_{X|C})^2\right)=E(X^2|C)-\left(E(X|C)\right)^2$

C라는 사건이 일어났을 때 X의 조건부 분산.

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