Permalink
Browse files

added probability measure

  • Loading branch information...
1 parent e369569 commit b40ffaa1844638225a76c380838fecc38a0d4b6b @ronert committed May 3, 2012
Showing with 10 additions and 1 deletion.
  1. +10 −1 cookbook.tex
View
@@ -304,7 +304,16 @@ \section{\T{Probability Theory}}
\item $\Pr{\displaystyle\bigsqcup_{i=1}^\infty A_i}
= \displaystyle\sum_{i=1}^\infty \Pr{A_i}$
\end{enumerate}
- \item \T{Probability space} $(\Omega,\mathcal{A},\prob)$
+ \item \T{Probability Space} $(\Omega,\mathcal{A},\prob)$
+ \item \T{Probability Measure}
+ \begin{enumerate}
+\item $\mathbb{P}(A)\geq 0\: \forall \: A\in\mathcal{B}$
+\item $\mathbb{P}$ is $\sigma$-additive for disjoint Events $A_{n}$
+\[
+\mathbb{P} \left( \bigcup\limits_{n=1}^{\infty} A_{n} \right)= \Sum[n=1]{\infty}\mathbb{P}(A_{n}).
+\]
+\item $\mathbb{P}(\Omega)=1$
+\end{enumerate}
\end{itemize}
\T{Properties}

0 comments on commit b40ffaa

Please sign in to comment.