5.3 �� (conditional probability) �� (independence)

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5.3 �� (conditional probability) �� (independence) - ��, 26/9/01

�� . �� ${{\bf {Pr}}\left[{B}\right]}>0$ ��

$\begin{displaymath} {{\bf {Pr}}\left[{A { \vert }B}\right]} = {{{\bf {Pr}}\left[{A \cap B}\right]} \over {{\bf {Pr}}\left[{B}\right]}}. \end{displaymath}$

�� $\cal A$ �� �� �� $A_1,\ldots,A_n \in {\cal A}$ ��

$\begin{displaymath} {{\bf {Pr}}\left[{A_1 \cap \cdots \cap A_n}\right]} = {{\bf ... ...t[{A_1}\right]}\cdot\ldots\cdot{{\bf {Pr}}\left[{A_n}\right]}. \end{displaymath}$

� �� .

�� $A_1, \ldots, A_n$ �� $\Omega$ �� (�� ) ��

$\begin{displaymath} {{\bf {Pr}}\left[{B}\right]} = \sum_{i=1}^n {{\bf {Pr}}\left[{B { \vert }A_i}\right]} {{\bf {Pr}}\left[{A_i}\right]}. \end{displaymath}$

Mihalis Kolountzakis

5.3 ���������� ��� ������� (conditional probability) ��� ����������� (independence) - ��, 26/9/01

5.3 �� (conditional probability) �� (independence) - ��, 26/9/01