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Definition: Random Experiments and Random Events

A random experiment is an experiment with the following properties:

• It is known, which outcomes it has, before it takes place, but
• is is generally unknown, which outcome it will have, until the experiment took place, and
• it is possible to find out, which outcome the experiment had after it took place.

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 \(A,B,C,\ldots\).

Table of Contents

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

Mentioned in:

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

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References

Bibliography

1. Bosch, Karl: "Elementare Einführung in die Wahrscheinlichkeitsrechnung", vieweg Studium, 1995, 6th Edition