The phrase "a unique probability" is correct and usable in written English.
It can be used in contexts where you want to emphasize that a particular probability is distinct or one-of-a-kind, often in statistical or mathematical discussions.
Example: "In this experiment, we calculated a unique probability for the occurrence of the rare event."
Alternatives: "a distinct likelihood" or "an exclusive chance".
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.
In fact, each data point would correspond to a unique probability density value that represents its likelihood or unique occurrence rate.
For a given set of such preferences, he generates a class of utility functions, each a positive linear transformation of the other (i.e. of the form U1 = aU2 + b, where a > 0), and a unique probability function.
Liu-Bai [26] proposed the concept of stochastically persistent in probability: there is a unique invariant probability measure μ such that (mu(Delta _{0})=0) and the distribution of (X t)) converges to μ as (t rightarrowinfty) whenever (X 0) inmathbb{R}_^{n}), where (Delta _{0}={ainmathbb{R}_^{n}|a_{i}=0mbox{ for some }i, 1leq ileq n}).
This equation can output a maximum of 128 unique probability estimates [ 16- 18].
In the case in which the transmission rate is varied and the error probability is kept fixed across different fading realizations, we have shown that the effective rate is maximized at a unique error probability.
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.
