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  2. De Morgan's laws - Wikipedia

    en.wikipedia.org/wiki/De_Morgan's_laws

    De Morgan's laws represented with Venn diagrams.In each case, the resultant set is the set of all points in any shade of blue. In propositional logic and Boolean algebra, De Morgan's laws, [1] [2] [3] also known as De Morgan's theorem, [4] are a pair of transformation rules that are both valid rules of inference.

  3. Independence (probability theory) - Wikipedia

    en.wikipedia.org/wiki/Independence_(probability...

    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.

  4. Boolean satisfiability problem - Wikipedia

    en.wikipedia.org/wiki/Boolean_satisfiability_problem

    For example, the formula "a AND NOT b" is satisfiable because one can find the values a = TRUE and b = FALSE, which make (a AND NOT b) = TRUE. In contrast, "a AND NOT a" is unsatisfiable. SAT is the first problem that was proven to be NP-complete—this is the Cook–Levin theorem.

  5. List of probabilistic proofs of non-probabilistic theorems

    en.wikipedia.org/wiki/List_of_probabilistic...

    Several results (for example, a continuum of mutually non-isomorphic models) are obtained by probabilistic means (random compact sets and Brownian motion). [ 26 ] [ 27 ] One part of this theory (so-called type III systems) is translated into the analytic language [ 28 ] and is developing analytically; [ 29 ] the other part (so-called type II ...

  6. Law of total probability - Wikipedia

    en.wikipedia.org/wiki/Law_of_total_probability

    In probability theory, the law (or formula) of total probability is a fundamental rule relating marginal probabilities to conditional probabilities. It expresses the total probability of an outcome which can be realized via several distinct events , hence the name.

  7. Statistical proof - Wikipedia

    en.wikipedia.org/wiki/Statistical_proof

    Bayesian statistics are based on a different philosophical approach for proof of inference.The mathematical formula for Bayes's theorem is: [|] = [|] [] []The formula is read as the probability of the parameter (or hypothesis =h, as used in the notation on axioms) “given” the data (or empirical observation), where the horizontal bar refers to "given".

  8. Notation in probability and statistics - Wikipedia

    en.wikipedia.org/wiki/Notation_in_probability...

    Random variables are usually written in upper case Roman letters, such as or and so on. Random variables, in this context, usually refer to something in words, such as "the height of a subject" for a continuous variable, or "the number of cars in the school car park" for a discrete variable, or "the colour of the next bicycle" for a categorical variable.

  9. Correlation - Wikipedia

    en.wikipedia.org/wiki/Correlation

    N.B.: the figure in the center has a slope of 0 but in that case, the correlation coefficient is undefined because the variance of Y is zero. In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data.