Definition: Independent Events
Let \(B\) be an event with the probability \(0 < p(B) < 1\). We call the event \(A\) independent from \(B\), if the conditional probability of \(A\) given \(B\) and the conditional probability of \(A\) given the complement event \(\overline{B}\) are equal each other:
\[p(A|B)=p(A|\overline{B}).\]
Loosely speaking, the frequency of occurrence of \(A\) does not depend on whether \(B\) happened, or not.
Table of Contents
- Proposition: Characterization of Independent Events
- Proposition: Characterization of Independent Events II
- Definition: Mutually Independent Events
- Definition: Pairwise Independent Events
Mentioned in:
Proofs: 1
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References
Bibliography
- Bosch, Karl: "Elementare Einführung in die Wahrscheinlichkeitsrechnung", vieweg Studium, 1995, 6th Edition