By Lothar Sachs (auth.)
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Extra resources for Applied Statistics: A Handbook of Techniques
Wolf's experiments with dice. 17035 (subjective probability). R. Wolf (1851) conducted an experiment in which a die was tossed 20,000 times. 146). 167. , Spinchorn 1970]). 2) originated with A. N. Kolmogorov (1933), who connected the notion of probability with modern set theory, measure theory, and functional analysis (cf. Van der Waerden 1951) and thereby created the theoretical counterpart to empirical relative frequency (cf. also Hemelrijk 1968, Rasch 1969, and Barnett 1973). 2 The addition theorem of probability theory The collection of possible outcomes of a surveyor an experiment forms the so-called space of elementary events, S.
Use paper on one side only; write all numbers clearly; leave wide margins for the rough work; avoid duplication; cross out any incorrect number and write the correct value above it. 3. Use rough estimates to avoid misplacing the decimal point; check your computation! Each arithmetical operation should be preceded or followed by a rough estimate, so that at least the location of the decimal point in the result is determined with confidence. 10- 2 . 67 . 413 . 10 - 2. 4. To double check, the problem should, if possible, be solved by still another method.
The space is thus finite. On the other hand, assume that in a game of Monopoly you land in jail. According to the rules you cannot move unless you toss a 6. Let an event consist of the number of times the die has to be tossed before a 6 comes up. Then, even in this simple situation, the space of elementary events is infinite, because every positive integer is a possible outcome (Walter 1966). If we are dealing with a characteristic of a continuous nature, such as the size of an object or the amount of rainfall, we can represent the events (outcomes) by points on the real axis.
Applied Statistics: A Handbook of Techniques by Lothar Sachs (auth.)