Search results
Results From The WOW.Com Content Network
Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes.Two events are independent, statistically independent, or stochastically independent [1] if, informally speaking, the occurrence of one does not affect the probability of occurrence of the other or, equivalently, does not affect the odds.
In probability theory, conditional independence describes situations wherein an observation is irrelevant or redundant when evaluating the certainty of a hypothesis. . Conditional independence is usually formulated in terms of conditional probability, as a special case where the probability of the hypothesis given the uninformative observation is equal to the probability
In mathematical logic, independence is the unprovability of some specific sentence from some specific set of other sentences. The sentences in this set are referred to as "axioms". The sentences in this set are referred to as "axioms".
It is often used in statistics as a tool to prove independence of two statistics, by first demonstrating one is complete sufficient and the other is ancillary, then appealing to the theorem. [2] An example of this is to show that the sample mean and sample variance of a normal distribution are independent statistics, which is done in the ...
Forcing was first used by Paul Cohen in 1963, to prove the independence of the axiom of choice and the continuum hypothesis from Zermelo–Fraenkel set theory. It has been considerably reworked and simplified in the following years, and has since served as a powerful technique, both in set theory and in areas of mathematical logic such as ...
k-wise independence has been used in theoretical computer science, where it was used to prove a theorem about the problem MAXEkSAT. k-wise independence is used in the proof that k-independent hashing functions are secure unforgeable message authentication codes.
Maren Morris is embracing a new era of independence, both in her professional and personal life.On Thursday, the Grammy-winning star drops an emotional cover of Billy Idol's "Dancing With Myself ...
Cohen [4] [7] showed that CH cannot be proven from the ZFC axioms, completing the overall independence proof. To prove his result, Cohen developed the method of forcing, which has become a standard tool in set theory. Essentially, this method begins with a model of ZF in which CH holds, and constructs another model which contains more sets than ...