Sentence examples for if there exists a probability from inspiring English sources

Now the question is if there exists a probability measure that simultaneously satisfies the first four probability assignments together with at least one probability assignment per each clause above.

David assigns the probability for each friend being at "Bar Phi": P phi_{A}) = 6/7,,P phi_{B}) = 5/7,, P phi_{C}) = 4/7, and the question is if there exists a probability measure that simultaneously satisfies these seven probability assignments.

there exist constants such that, if, there exists an element with.

These theorems show that if preferences among acts meet certain constraints, such as transitivity, then there exist a probability function and a utility function (given a choice of scale) that generate expected utilities agreeing with preferences.

A preferential consequence relation is admissible if and only if, for every ε > 0, there exists a probability function P such that, for all propositions p and q, p q iff P q/p) ≥ 1 − ε. 6.

According to Rao and Ephremides [22], a queue is stable if and only if there exists a positive probability for the queue being empty, i.e., lim t → ∞ Pr Q i ( t ) = 0 > 0, (7).

There is now a bubble in the market at a stopping time τ if there exists a scenario (a probability measure (bar {{mathbb {Q}}}in {mathcal {P}})) such that the robust fundamental value is smaller than the market value with positive probability and all probabilities that coincide with (bar {{mathbb {Q}}}) on ({mathcal {F}}_{tau }) agree on this view.

If there exists a unique invariant probability measure V satisfying (V(Delta_{0})=0) and the distribution of (X t)) converges to V as (trightarrow+infty ) whenever (X(0)inmathbb{R}^{n}_), where (Delta_{0}={ain overline{mathbb{R}}^{n}_|a_{i}=0 text{ for some } i, 1leq ileq n}), then (16) is stochastically persistent in probability.

A group (G) is amenable if there exists a left-invariant finitely additive probability measure defined on all subsets of (G) (there are many other equivalent definitions).

Alternatively, the function ρ is a coherent risk measure if and only if there exists a nonempty set (mathcal {Q}) of probability measures, absolutely continuous with respect to P, such that rho(X) = -inf_{Qinmathcal{Q}}E^{Q}[X].

In other words, a separating hyperplane exists only if there exists a linear relation among n given functions with probability one.