WÜRFEL, ZUFALL UND WAHRSCHEINLICHKEIT: EIN BLICK AUF DIE VORGESCHICHTE DER STOCHASTIK

Es ist üblich, die Ursprünge der Wahrscheinlichkeitsrechnung in verschiedenen Arbeiten zu sehen, die im 17.Jahrhundert entstanden sind. Nun kann man sich natürlich fragen, ob nicht einige der Begriffe und Überlegungen, die heute zur Stochastik gehören, schon früher vorhanden gewesen sind. In dieser Arbeit versuchen wir, diese Frage zu beantworten: Wir skizzieren den Wahrscheinlichkeitsbegriff, der in der Antike, im Mittelalter und in der frühen Neuzeit zu finden ist und gehen der Beurteilung von Chancen durch Auszählen der günstigen Fälle und frühen Feststellungen von statistischer Regelmäßigkeit nach

Diminished mental- and physical function and lack of social support are associated with shorter survival in community dwelling older persons of Botswana

<p>Abstract</p> <p>Background</p> <p>Mortality rates for older persons in Botswana have been unavailable and little is known of predictors of mortality in old age. This study may serve as a precursor for more detailed assessments.</p> <p>The objective was to assess diminished function and lack of social support as indicators of short term risk of death.</p> <p>Methods</p> <p>A national population based prospective survey was undertaken in Botswana; twelve rural areas and three urban centers were included.</p> <p>372 community-dwelling persons aged sixty years and over, were included; 265 were followed-up. Sixteen subjects were deceased at follow-up.</p> <p>Subjects were interviewed and clinically assessed at home. Measures of cognitive function, depression and physical function and sociodemographic information were collected. Subjects were followed-up at average 6.8 months after baseline.</p> <p>Results</p> <p>Overall mortality rate was 10.9 per 100 person years. Age-adjusted odds ratios (OR) for death during follow-up were; 4.2 (CI 1.4–12.5) and 3.6 (CI 1.0–12.7) for those with diminished physical- and cognitive function, respectively.</p> <p>Indicators of limited social support; household with only 1 or 2 persons and eating alone, yielded age adjusted ORs of 4.3 (CI 1.5–12.5) and 6.7 (CI 2.2–20), respectively, for death during follow-up.</p> <p>Conclusion</p> <p>Older community dwelling persons with diminished cognitive- or physical function, solitary daily meals and living in a small household have a significantly increased risk of rapid deterioration and death.</p> <p>Health policy should include measures to strengthen informal support and expand formal service provisions to older persons with poor function and limited social networks in order to prevent premature deaths.</p

Der schlechte Würfel—Ein selten behandeltes problem in der geschichte der stochastik

AbstractThefair die, a tool used by probabilists to generate uniform distributions, goes back to the early history of probability theory. Thecrooked (biased) die was introduced later by Newton and studied in a work of Simpson (1740) as one of the first problems in geometric probability. More recently, R. Wolf (1881) and E. Heilbronner (1984/1985) were able, under reasonable assumptions, to predict the probability of simple events related to particular crooked dice