# Probability on Finite and Discrete Set and Uniform Distribution

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## Probability on Finite and Discrete Set and Uniform Distribution

A pseudorandom number generator plays an important role in practice in computer science. For example: computer simulations, cryptology, and so on. A pseudorandom number generator is an algorithm to generate a sequence of numbers that is indistinguishable from the true random number sequence. In this article, we shall formalize the "Uniform Distribution" that is the idealized set of true random number sequences. The basic idea of our formalization is due to [15].

[1] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.

[2] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.

[3] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.

[4] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.

[5] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.

[6] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.

[7] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.

[8] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.

[9] Czesław Byliński. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990.

[10] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.

[11] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.

[12] Andrzej Nędzusiak. Probability. Formalized Mathematics, 1(4):745-749, 1990.

[13] Jan Popiołek. Introduction to probability. Formalized Mathematics, 1(4):755-760, 1990.

[14] Piotr Rudnicki. Little Bezout theorem (factor theorem). Formalized Mathematics, 12(1):49-58, 2004.

[15] Victor Shoup. A computational introduction to number theory and algebra. Cambridge University Press, 2008.

[16] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.

[17] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.

[18] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.

[19] Bo Zhang and Yatsuka Nakamura. The definition of finite sequences and matrices of probability, and addition of matrices of real elements. Formalized Mathematics, 14(3):101-108, 2006, doi:10.2478/v10037-006-0012-1.

# Formalized Mathematics

## (a computer assisted approach)

### Journal Information

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Target Group

researchers in the fields of formal methods and computer-checked mathematics

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