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The principle can be viewed as an example of the sieve method extensively used in number theory and is sometimes referred to as the sieve formula. [ 4 ] As finite probabilities are computed as counts relative to the cardinality of the probability space , the formulas for the principle of inclusion–exclusion remain valid when the cardinalities ...
The count–min sketch was invented in 2003 by Graham Cormode and S. Muthu Muthukrishnan [1] and described by them in a 2005 paper. [ 2 ] Count–min sketch is an alternative to count sketch and AMS sketch and can be considered an implementation of a counting Bloom filter (Fan et al., 1998 [ 3 ] ) or multistage-filter . [ 1 ]
One example of the double counting method counts the number of ways in which a committee can be formed from people, allowing any number of the people (even zero of them) to be part of the committee. That is, one counts the number of subsets that an -element set may have. One method for forming a committee is to ask each person to choose whether ...
To generate a member of the sequence from the previous member, read off the digits of the previous member, counting the number of digits in groups of the same digit. For example: 1 is read off as "one 1" or 11. 11 is read off as "two 1s" or 21. 21 is read off as "one 2, one 1" or 1211. 1211 is read off as "one 1, one 2, two 1s" or 111221.
Graphical examination of count data may be aided by the use of data transformations chosen to have the property of stabilising the sample variance. In particular, the square root transformation might be used when data can be approximated by a Poisson distribution (although other transformation have modestly improved properties), while an inverse sine transformation is available when a binomial ...
In mathematics, specifically measure theory, the counting measure is an intuitive way to put a measure on any set – the "size" of a subset is taken to be the number of elements in the subset if the subset has finitely many elements, and infinity if the subset is infinite.
is the generating function of the set of colors, so that there are f w colors of weight w for each integer w ≥ 0. In the multivariate case, the weight of each color is a vector of integers and there is a generating function f(t 1, t 2, ...) that tabulates the number of colors with each given vector of weights.
For example, in the interval [,] fat Cantor sets, like the Smith–Volterra–Cantor set, are closed nowhere dense and they can be constructed with a measure arbitrarily close to The union of a countable number of such sets with measure approaching 1 {\displaystyle 1} gives a meagre subset of [ 0 , 1 ] {\displaystyle [0,1]} with measure 1 ...