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In mathematics, the distributive property of binary operations is a generalization of the distributive law, which asserts that the equality (+) = + is always true in elementary algebra.
In mathematics, summation is the addition of a sequence of numbers, called addends or summands; the result is their sum or total.Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials and, in general, elements of any type of mathematical objects on which an operation denoted "+" is defined.
A random variable X has a Bernoulli distribution if Pr(X = 1) = p and Pr(X = 0) = 1 − p for some p ∈ (0, 1).. De Finetti's theorem states that the probability distribution of any infinite exchangeable sequence of Bernoulli random variables is a "mixture" of the probability distributions of independent and identically distributed sequences of Bernoulli random variables.
In number theory, Ramanujan's sum, usually denoted c q (n), is a function of two positive integer variables q and n defined by the formula = (,) =,where (a, q) = 1 means that a only takes on values coprime to q.
In mathematics, a distributive lattice is a lattice in which the operations of join and meet distribute over each other. The prototypical examples of such structures are collections of sets for which the lattice operations can be given by set union and intersection.
In addition, it is known that the following statements are equivalent for any complete lattice L: [2]. L is completely distributive.; L can be embedded into a direct product of chains [0,1] by an order embedding that preserves arbitrary meets and joins.
The typical diagram of the definition of a universal morphism. In mathematics, more specifically in category theory, a universal property is a property that characterizes up to an isomorphism the result of some constructions.
Let {x i} be a set of random variables with a Rademacher distribution.Let {a i} be a sequence of real numbers.Then (> ‖ ‖) /where ||a|| 2 is the Euclidean norm of the sequence {a i}, t > 0 is a real number and Pr(Z) is the probability of event Z.