Updated 2017-10-20
\(\Omega\) is the set of all possible outcomes. An event is a subset of \(\Omega\).
Events \(A\) and \(B\) are mutually exclusive if and only if \(\mathbb P(A\cup B)=\mathbb P(A)+\mathbb P(B)\).
Events \(A\) and \(B\) are independent if and only if \(\mathbb P(A\cap B)=\mathbb P(A)\mathbb P(B)\).
Probability of event \(A\) given \(B\) is \(\mathbb P(A\vert B)=\frac{\mathbb P(A\cap B)}{\mathbb P(B)}\), \(\mathbb P(B)\neq 0\).
For all mutually exclusive events \(B_i\) that partitions \(\Omega\), the probability of event \(A\) is \(\mathbb P(A)=\sum A\cap B_i\).
Random variable maps outcomes \(\omega \in \Omega\) of a probabilistic experiment to a real number \(X(\omega)\in\mathbb R\)
Properties:
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