Sentence examples for expectation of the function from inspiring English sources

where E[f x,y)] denotes the empirical expectation of the function.

where 〈 f (x)〉p(x)= ∫ p (x) f (x) dx is the expectation of the function f(x) with respect to p(x).

with initial condition Θ(0)=a, where P Θ n is the n-step transition function of the Markov chain J k with DFE Θ, and P Θ n H Θ ( j, y ′ ) is the expectation of the function H Θ (G) (defined in (3)) using the conditional measure P Θ n(.|j,y′)(Note G k is a fixed function of J k ).

Expressed in words, the expectation of the propensity function on left-hand side of equation (29) equals its rate function, and the rate function can be directly used as propensity function in stochastic simulations.

Further, a method of the proof is also new and interesting, which is to use the mathematical expectation of the distribution function studying the related problems.

The expectation of the value function is driven by stochastic differential equation (19).

As is well known, Jensen's inequality provides an upper bound for the expectation of the log function.

An H2 optimal control problem is formulated as a "minmax" problem of the expectation of the cost function with respect to the stochastic noise in the identified parameters.

This sampling method offers a direct approximate inference of the expectation of the target function with respect to a probability distribution [17].

The selection probability often needs to be estimated for the IPW estimator, and both the selection probability and the conditional expectation of the score function needs to be estimated for the AIPW estimator.

Assuming an uniformly distributed residual frequency offset, we obtain the average SNR by taking the expectation of the sinc function over the random f Δ, i.e., E sinc 2 π f Δ T p = ∫ - f c f c sinc ( 2 π x T p ) p ( x ) d x (40).