Wurfergebnisses

Wurfergebnisses is a term used in discussions of probability, statistics and gaming to refer to the outcomes produced by a throwing process. The concept covers both a single throw and the set of results obtained from multiple throws. The word combines Wurf (throw) and Ergebniss/Ergebnis (result). In standard German, the more common terms are Wurfergebnis (singular) and Wurfergebnisse (plural); Wurfergebnisses is seen mainly in older texts or as a stylistic variant and is not the dominant form in modern usage.

In formal terms, a single Wurfergebnis is an element of the sample space S. For n throws, the Wurfergebnisse is the sequence (x1, ..., xn) or the multiset of outcomes, depending on whether order matters. Probability theory describes this via a distribution on S^n, or via a random variable X representing the outcome of a single throw and its distribution. The frequency of observed Wurfergebnisse converges to the underlying probabilities according to the law of large numbers.

Usage and interpretation: The term is mainly used in didactic contexts or game rules to refer to the observed outcome of a throw or the results across several throws. It is important to distinguish between a single Wurfergebnis and the empirical frequencies of many Wurfergebnisse.

Examples: Rolling a fair six-sided die once yields a Wurfergebnis of one of {1,2,3,4,5,6} with probability 1/6. Rolling the die twice yields Wurfergebnisse such as (3,5).

See also: probability distribution, random variable, sample space, trial, event, empirical frequency.