Definition: Random Experiments and Random Events

A random experiment is an experiment with the following properties:

The set of all outcomes is called probability space and denoted by \(\Omega\).

Any subset \(F\subseteq \Omega\) of outcomes is called a random event or just event. We denote events, using Latin capital letters \(A,B,C,\ldots\).

Explanations: 1

  1. Definition: Certain and Impossible Event
  2. Proposition: Probability of the Complement Event
  3. Proposition: Probability of Included Event
  4. Proposition: Probability of Event Difference
  5. Proposition: Probability of Event Union
  6. Proposition: Probability of Joint Events

Definitions: 1 2 3 4 5 6 7 8 9 10 11 12 13
Explanations: 14 15
Proofs: 16 17 18 19 20 21 22 23
Propositions: 24 25 26 27 28 29 30 31 32 33
Theorems: 34


Thank you to the contributors under CC BY-SA 4.0!

Github:
bookofproofs


References

Bibliography

  1. Bosch, Karl: "Elementare Einf├╝hrung in die Wahrscheinlichkeitsrechnung", vieweg Studium, 1995, 6th Edition