Sentence examples for trivial probability from inspiring English sources

Further, when ( Ω, F, P ) is a trivial probability space every element in Ehas merely the two trivial stratifications since F = ; when ( Ω, F, P ) is arbitrary, every element in E can possessarbitrarily many nontrivial intermediate stratifications.

When the base space ( Ω, ℱ, P ) of the RN module is a trivial probability space, i.e., ℱ = { Ω, 0̸ }, the new version of the Gleason-Kahane-Żelazko theorem automatically degenerates to the classical case.

This yields a trivial probability function which maps all the Pα to either 1 or 0, and, provided that values 1 and 0 both occur (which follows trivially from interpreting the numbers as probabilities), this function must clearly be discontinuous (cf. Redhead 1987: 28).

Modes at 1 and 0 indicate a non-trivial probability of one team winning or losing every event, which is more common when only a few events occur.

But given the 'narrative potential' [ 8] of any given gene, as well as the non-trivial probability that a candidate mutation will be functional at the molecular level but not causal for the phenotype being investigated, the bar must be set extremely high for declaring success.

It is easy — all too easy — to assign equal probabilities to the points in such a space: each gets probability 0. Non-trivial probabilities arise when uncountably many of the points are clumped together in larger sets.

Since classical statistics employs non-trivial probabilities that attach to the single case in its procedures, a fully frequentists understanding of statistics is arguably in need of a response to the reference class problem.

(The caveat "non-trivial" is added here because on some accounts all future events that actually happen have probability, conditional on past history, equal to 1, and future events that do not happen have probability equal to zero. Non-trivial probabilities are probabilities strictly between zero and one).

Individuals assigned to two sources with non-trivial probabilities were considered putative hybrids.

However, by using recurrence relation [48], [49] all the seeming drawbacks are trivial and probability (6) can be evaluated very readily.

The non-negativity and normalization axioms are largely matters of convention, although it is non-trivial that probability functions take at least the two values 0 and 1, and that they have a maximal value (unlike various other measures, such as length, volume, and so on, which are unbounded).