Von Mises never totally formalized his definition of a proper selection rule for sub-sequences, but in 1940 Alonzo Church defined it as any recursive function which having read the first N elements of the sequence decides if it wants to select element number N + 1. is not biased, by selecting the odd positions, we get 000000. The sub-sequence selection criterion imposed by von Mises is important, because although 0101010101. the frequency of zeros goes to 1/2 and every sub-sequence we can select from it by a "proper" method of selection is also not biased. Using the concept of the impossibility of a gambling system, von Mises defined an infinite sequence of zeros and ones as random if it is not biased by having the frequency stability property i.e. In 1919 Richard von Mises gave the first definition of algorithmic randomness, which was inspired by the law of large numbers, although he used the term collective rather than random sequence. Émile Borel was one of the first mathematicians to formally address randomness in 1909. The Bourbaki school considered the statement "let us consider a random sequence" an abuse of language. Traditional probability theory does not state if a specific sequence is random, but generally proceeds to discuss the properties of random variables and stochastic sequences assuming some definition of randomness. Īxiomatic probability theory deliberately avoids a definition of a random sequence. in which each term is unpredictable to the uninitiated and whose digits pass a certain number of tests traditional with statisticians". Lehmer stated in 1951: "A random sequence is a vague notion. The concept generally relies on the notion of a sequence of random variables and many statistical discussions begin with the words "let X 1., X n be independent random variables.". The concept of a random sequence is essential in probability theory and statistics.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |