Sentence examples for unique probability from inspiring English sources

A basic theorem says that there is a suitable σ-field containing all the intervals and a unique probability defined on this σ-field for which the probability of an interval is its length.

By their definition, they imply a unique probability density function.

The precise characterization of the RES output by means of a unique probability distribution is a challenging task.

Savage showed that whenever these six axioms are satisfied, the comparative belief relation can be represented by a unique probability function.

We construct a fusion frame {W, w} such that its dual fusion frame {W, v} is the unique probability optimal dual frames in some cases.

In fact, each data point would correspond to a unique probability density value that represents its likelihood or unique occurrence rate.

Our results show that, although tetrasomic inheritance creates additional configurations of lineages that have unique probabilities of coalescence compared to those for diploid organisms, the ancestral process for autotetraploids without double reduction converges to Kingman's haploid coalescent model with time rescaled by 4 N generations.

The attribute matching method utilized 267 of the 512 possible unique pretest probability estimates to yield a median pretest probability value of 5.5% (1st 3rd quartiles: 1.0 10.5%).

A hazard rate implies a unique conventional probability density and its cumulative distribution.

For a strong Feller and irreducible Markov semigroup on a locally compact Polish space, the Harnack-type inequality (1.1) holds if and only if the semigroup has a unique invariant probability measure and is ultracontractive.

If the external force is the gradient of a convex potential, it has been proved that the process converges towards the unique invariant probability as the time goes to infinity.