What is a probability space?
Q: What is a probability space?
A: A probability space is a mathematical model used to describe scientific experiments. It consists of three parts: a sample space which lists all possible outcomes, a set of events that associate zero or more outcomes, and a function that assigns probabilities to each event.
Q: What does the sample space consist of?
A: The sample space consists of all possible outcomes, often written as Ω {\displaystyle \Omega } , and an outcome as ω {\displaystyle \omega } .
Q: What is an outcome?
A: An outcome is the result of a single execution of the model.
Q: What are events used for in probability spaces?
A: Events are used to characterize groups of outcomes since individual outcomes might be of little practical use. The collection of all such events is called a σ-algebra, sometimes written as F {\displaystyle {\mathcal {F}}} .
Q: How are probabilities assigned to each event?
A: Probabilities are assigned to each event using the probability measure function P.
Q: Who introduced the notion of probability spaces? A: The prominent Soviet mathematician Andrey Kolmogorov introduced the notion of probability spaces together with other axioms of probability in the 1930s.
