Sample space

As a result, space, result set result set or sample space is referred to in the mathematical subfield of stochastics the set of all possible outcomes of a random experiment. For a description of such an experiment using a probability space certain subsets of the sample space, events, probabilities are assigned.

To set up the case of multistage random experiments a suitable sample space can be used as a convenient tool sometimes a decision tree.

Examples

• When dice with a dice is the result space: Ω = { 1,2,3,4,5,6 }
• In the simple coin toss is the result space: Ω = {K, Z }; (K = head, Z = number )
• At the same time tossing two distinguishable coins is the result space: Ω = { Kk, Kz, Zz, kZ }; (K = head, Z = number of (large coin), k = head, z = number of (small coin) )
• It is quite possible that there is a random experiment two or more reasonable result areas. One example, consider the random experiment to draw a card from a deck, then the result set of the card values ​​(Ace, 2, 3, ...) or the color values ​​( clubs, spades, hearts, diamonds ) include. A full list of the results, however, would take into account both the card value as well as the color. A corresponding result set can be generated as a Cartesian product of the two previous result sets.

Importance

To calculate the probability of discrete events according to Laplace knowledge of the cardinality of the sample space is absolutely necessary. Result rooms also occur with probability spaces. A probability space is based on a sample space, but defines a set of "interesting events", the algebra of events on which the probability measure is defined. For a more explicit representation of the context and with an example see the article in probability theory.

Confused terminology: event space - the outcome space

In the literature it is not always carefully distinguished between the concepts of sample space and outcome space. Therefore, it happens that the sample space is called an event space.