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In the case when the probability of loss is assumed to be a single number , and is the loss from the event occurring, the familiar form of the Hand formula is recovered. More generally, for continuous outcomes the Hand formula takes form: ∫ Ω L f ( L ) d L > B {\displaystyle \int _{\Omega }Lf(L)dL>B} where Ω {\displaystyle \Omega } is the ...
In probability theory, a transition-rate matrix (also known as a Q-matrix, [1] intensity matrix, [2] or infinitesimal generator matrix [3]) is an array of numbers describing the instantaneous rate at which a continuous-time Markov chain transitions between states.
A quasi Fermi level is a term used in quantum mechanics and especially in solid state physics for the Fermi level (chemical potential of electrons) that describes the population of electrons separately in the conduction band and valence band, when their populations are displaced from equilibrium.
Paschen's law is an equation that gives the breakdown voltage, that is, the voltage necessary to start a discharge or electric arc, between two electrodes in a gas as a function of pressure and gap length.
It is most often used to model resonances (unstable particles) in high-energy physics. In this case, E is the center-of-mass energy that produces the resonance, M is the mass of the resonance, and Γ is the resonance width (or decay width), related to its mean lifetime according to τ = 1 / Γ. (With units included, the formula is τ = ħ / Γ.)
In probability theory, Isserlis' theorem or Wick's probability theorem is a formula that allows one to compute higher-order moments of the multivariate normal distribution in terms of its covariance matrix. It is named after Leon Isserlis.
The probability distribution according to Metropolis-Hastings Dynamics for the change in energy that would result from flipping some spin s for different temperatures, T. () =. Although both of the acceptance probabilities approximate a step curve and they are almost indistinguishable at very low temperatures, they differ when temperature gets ...
The change in entropy in the entropy of mixing example may be viewed as an example of a non-extensive entropy resulting from the distinguishability of the two types of particles being mixed. Quantum particles are either bosons (following Bose–Einstein statistics ) or fermions (subject to the Pauli exclusion principle , following instead Fermi ...