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The rule of sum is an intuitive principle stating that if there are a possible outcomes for an event (or ways to do something) and b possible outcomes for another event (or ways to do another thing), and the two events cannot both occur (or the two things can't both be done), then there are a + b total possible outcomes for the events (or total possible ways to do one of the things).
In combinatorics, the rule of division is a counting principle. It states that there are n/d ways to do a task if it can be done using a procedure that can be carried out in n ways, and for each way w, exactly d of the n ways correspond to the way w. In a nutshell, the division rule is a common way to ignore "unimportant" differences when ...
where the rule is that wherever an instance of "()" appears on a line of a proof, it can be replaced with "()", and vice versa. Import-export is a name given to the statement as a theorem or truth-functional tautology of propositional logic:
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".
In propositional logic, disjunction elimination [1] [2] (sometimes named proof by cases, case analysis, or or elimination) is the valid argument form and rule of inference that allows one to eliminate a disjunctive statement from a logical proof.
This proposition is (sometimes) known as the law of the unconscious statistician because of a purported tendency to think of the aforementioned law as the very definition of the expected value of of a function g(X) and a random variable X, rather than (more formally) as a consequence of the true definition of expected value. [1]
The Sturm chain or Sturm sequence of a univariate polynomial P(x) with real coefficients is the sequence of polynomials ,, …, such that =, = ′, + = (,), for i ≥ 1, where P' is the derivative of P, and (,) is the remainder of the Euclidean division of by .
In statistics, the Lehmann–Scheffé theorem is a prominent statement, tying together the ideas of completeness, sufficiency, uniqueness, and best unbiased estimation. [1] The theorem states that any estimator that is unbiased for a given unknown quantity and that depends on the data only through a complete , sufficient statistic is the unique ...