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Download The Classical Differential Geometry of Curves and Surfaces by Georges Valiron PDF

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By Georges Valiron

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Example text

The perfect randomizer does not exist in practice. There are, however, devices that come close to a randomizer. They serve the purpose of a randomizer. The proof of the pudding is in the eating: the people living in the princedom of Monaco do not pay taxes as the randomizers in the casino of Monaco provide sufficient income for the princedom. A simple example of a randomizer is a coin. The two outcomes “heads” and “tails” are equally probable. Another example of a randomizer is a dice. Each of the numbers 1–6 has the same probability, provided the dice is “fair” (Fig.

In this book, the term “representative” is used only in one way: a sample is said to be representative with respect to a variable if its relative distribution in the sample is equal to its relative distribution in the population. For example, a sample is representative with respect to the variable gender, if the percentages of males and females in the sample are equal to the percentages of males and females in the population. The foundations of survey sampling learn that samples have to be selected with some kind of probability mechanism.

A roulette wheel is a good example of sampling with replacement. At every turn, each of the possible numbers can again be produced with the same probability. It is possible (but not very likely) that in a sequence of 10 turns, the number 7 is produced 10 times (Fig. 7). A simple example illustrates sampling with replacement. Suppose, the population consists of four elements: U ¼ {1, 2, 3, 4}. Then the possible samples of size 2 are as follows: (1, 1) (2, 1) (3, 1) (4, 1) (1, 2) (2, 2) (3, 2) (4, 2) (1, 3) (2, 3) (3, 3) (4, 3) (1, 4) (2, 4) (3, 4) (4, 4) So a sampling design describes which samples a from U are possible.

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