zufälligen

zufälligen is the genitive singular masculine or neuter form of the German adjective zufällig, which translates to "random" or "accidental" in English. This grammatical form indicates possession or a relationship of origin when referring to a masculine or neuter noun in the singular that is governed by the genitive case. For example, in the phrase "die Farbe des zufälligen Ergebnisses," "zufälligen" modifies "Ergebnisses" (result), denoting the color belonging to or arising from the random outcome. Similarly, in "die Ursache des zufälligen Vorfalls," it describes the cause of the accidental incident. The adjective itself describes something that occurs without a predetermined cause or plan, often due to chance. In statistical contexts, zufällig is crucial for concepts like random sampling or random variables, where unpredictability is a key characteristic. The genitive case in German is often used to express belonging, origin, or a part-whole relationship, and "zufälligen" in this form specifies that the described noun is connected to something that is random or accidental.