5.7 �� . �� (��).

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5.7 �� . �� (��). - �� 4/10/2001

�� (��. 2.4).

�� §2.5 (�� ) �� (3/10/2001) �� -�� (inlusion-exclusion principle) �� :

$\begin{displaymath} {{\bf {Pr}}\left[{A \cup B}\right]} = {{\bf {Pr}}\left[{A}\r... ...f {Pr}}\left[{B}\right]} - {{\bf {Pr}}\left[{A\cap B}\right]}. \end{displaymath}$

�� §2.5 �� .

�� (��) �� . �� (�� ) �� . �� $\Omega$ , ��

$\begin{displaymath} X: \Omega \to {\mathbf Z}. \end{displaymath}$

�� (�� , �� ) ��

$\begin{displaymath} f_X(k) = {{\bf {Pr}}\left[{X = k}\right]}, (k\in{\mathbf Z}). \end{displaymath}$

�� $f_X:{\mathbf Z}\to[0,1]$ �� ��  ��

��

$\begin{displaymath} \sum_{k\in{\mathbf Z}} f_X(k) = 1. \end{displaymath}$

� �� ��  �� (expectation)

$\begin{displaymath} {{\bf E}\left[{X}\right]} = \sum_{k\in{\mathbf Z}} k\cdot {{... ...r}}\left[{X=k}\right]} = \sum_{k\in{\mathbf Z}} k\cdot f_X(k). \end{displaymath}$

� �� �� �� , ��

$\begin{displaymath} \sum_{k\in{\mathbf Z}} {\left\vert{k}\right\vert} f_X(k) < \infty. \end{displaymath}$

�� . �� , �� . �� (�� . �� 0 �� ) �� .

Mihalis Kolountzakis

5.7 ������ ����� ��� �� �������. ������� ���������� (���������). - �� 4/10/2001

5.7 �� . �� (��). - �� 4/10/2001