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The simplest approach is to add one to each observed number of events, including the zero-count possibilities. This is sometimes called Laplace's rule of succession. This approach is equivalent to assuming a uniform prior distribution over the probabilities for each possible event (spanning the simplex where each probability is between 0 and 1 ...
The characteristic function + = ((+)) of the sum of two independent random variables X and Y is just the product of the two separate characteristic functions: = (), = ()
Cayley's formula implies that there is 1 = 2 2 − 2 tree on two vertices, 3 = 3 3 − 2 trees on three vertices, and 16 = 4 4 − 2 trees on four vertices. Adding a directed edge to a rooted forest. What is the number of different trees that can be formed from a set of distinct vertices?
In words, to count the number of elements in a finite union of finite sets, first sum the cardinalities of the individual sets, then subtract the number of elements that appear in at least two sets, then add back the number of elements that appear in at least three sets, then subtract the number of elements that appear in at least four sets ...
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Number blocks, which can be used for counting. Counting is the process of determining the number of elements of a finite set of objects; that is, determining the size of a set. . The traditional way of counting consists of continually increasing a (mental or spoken) counter by a unit for every element of the set, in some order, while marking (or displacing) those elements to avoid visiting the ...
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A counting Bloom filter is a probabilistic data structure that is used to test whether the number of occurrences of a given element in a sequence exceeds a given threshold. As a generalized form of the Bloom filter, false positive matches are possible, but false negatives are not – in other words, a query returns either "possibly bigger or equal than the threshold" or "definitely smaller ...