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Tag Archives: sampling
Bijective proofs
A fourth proof Last month I described three proofs of the formula for the number of ways to choose k objects from a set of n, if repetition is allowed and order is not significant; it is the same as … Continue reading
Posted in exposition, open problems
Tagged bijections, Catalan numbers, Catalan objects, Dima FonDerFlaass, permutations, sampling
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Another formula
Anyone who knows about the Principle of Inclusion and Exclusion will suspect that it can be applied to the relationship between sampling with and without replacement. In order to find the formula for sampling without replacement, we must be able … Continue reading
Three formulae
Yesterday, we sampled k objects from a set of n under four possible sampling rules. Suppose that the n objects are of two different types, A and B, with a of type A and b of type B, where a+b = n. … Continue reading
Three proofs
In how many ways can you choose a sample of size k from n distinguishable objects? As is well known, the answer depends on the sampling rules: Does the order of selection matter, or not? Are items allowed to be … Continue reading
Lists
In Notes from Overground, Tiresias (my former neighbour Roger Green) quotes with approval from a lecture by W. H. Auden, on “four questions which, could I examine a critic, I should ask him”. He said: He said: ‘If a critic could truthfully … Continue reading