- Cumulative distribution function, in which the probability of a value is a function of that value

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In abstract algebra and formal logic, the **distributive property** of binary operations generalizes the **distributive law** from elementary algebra. In propositional logic, **distribution** refers to two valid rules of replacement. The rules allow one to reformulate conjunctions and disjunctions within logical proofs.

For example, in arithmetic:

In the left-hand side of the first equation, the 2 multiplies the sum of 1 and 3; on the right-hand side, it multiplies the 1 and the 3 individually, with the products added afterwards.
Because these give the same final answer (8), it is said that multiplication by 2 *distributes* over addition of 1 and 3.
Since one could have put any real numbers in place of 2, 1, and 3 above, and still have obtained a true equation, we say that multiplication of real numbers *distributes* over addition of real numbers.

Given a set *S* and two binary operators ∗ and + on *S*, we say that the operation:

∗ is *left-distributive* over + if, given any elements *x*, *y*, and *z* of *S*,

This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Distributive_property

In probability and statistics, a **probability distribution** assigns a probability to each measurable subset of the possible outcomes of a random experiment, survey, or procedure of statistical inference. Examples are found in experiments whose sample space is non-numerical, where the distribution would be a categorical distribution; experiments whose sample space is encoded by discrete random variables, where the distribution can be specified by a probability mass function; and experiments with sample spaces encoded by continuous random variables, where the distribution can be specified by a probability density function. More complex experiments, such as those involving stochastic processes defined in continuous time, may demand the use of more general probability measures.

In applied probability, a probability distribution can be specified in a number of different ways, often chosen for mathematical convenience:

This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Probability_distribution

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