1. adj. (of a system of linear equations or a set of vectors), see linearly independent. 2. (Statistics) a. (of two or more random variables) distributed so that the value of one variable will have no effect on that taken by the others. Thus the probability of each random variable taking each of some sequence of specified values equals the product of their sepa rate probabilities of taking these values. More formally and generally, for random variables X₁,...,X_n on a given probability space with values in a real or complex Euclidean space it is required that for arbitrary Borel sets B₁,..., B_n.
b. (of two or more events) such that the occurrence of one does not affect the probability of any of the others. Consequently, the probability of any set of independent events occurring equals the product of their individual probabilities. Comp are statistically dependent. 3. (Logic) (of a set of statements, propositions, or formulae) a. not validly derivable from one another or from any set of the others, so that if all are axioms of some theory, none can be dispensed with without loss.
b. more generally, not logically related, so that in no case can the truth value of one be inferred from those of the others. 4. (of a set of measurable functions, {f_γ}_γ∈Γ, from a measure set X with μ(X) = 1 to Rⁿ) such thatfor every finite collection, A₁,..., A_k, of Borel sets in Rⁿ and any collection γ₁,..., γ_k of indices.