Sentence examples for sample problems with from inspiring English sources
Sample problems with detailed solutions are illustrated.
Numerical results are shown for sample problems with the Mie Grüneisen equation of state for characterizing the materials of interests in both one and two space dimensions that demonstrate the feasibility of the proposed method for interface-sharpening of compressible two-phase flow.
There were sample problems with a flat gamma prior for the smoothness parameter σ 1 2.
So there's another sample problem with the notes, which is sort of like a standard problem.
Otherwise, if we reject the null hypothesis of homogeneity in (1), the hypothesis to be tested is (2) H 0 : μ 1 = μ 2 subject to Σ 1 ≠ Σ 2. This is the usual test for equality of means in a two sample problem with unequal covariance matrices, also called Behrens-Fisher problem (see [ 25]).
For small samples (problems with fewer than 400 units and up to three outputs and three inputs), Algorithm #1 fits results better than Algorithm #2, which is more efficient as of samples that exceed 800 units.11 Since the samples analyzed in our research are made up of around a hundred schools, we apply the simple Algorithm #1, which is described below.12.
In this sense, this parametric Bayesian approach is promising because it turns the time-consuming optimization problem into a simple sampling problem with a fast and stable Gibbs sampling scheme.
This was identified as a difficult computational problem [ Ghosh et al., 2008], but if we assume that the standard errors of the stage 1 and 2 estimates are fixed and known, this reduces to a sampling problem with weights given by the marginal power of each SNP.
Sample problems are provided together with numerical solutions and explanations of their application.
New operations are presented at the top of each sheet, sometimes with sample problems and a cursory explanation.
Given that standardized tests have served me so well, I approached the Partnership for Assessment of College and Career Readiness (PARCC) sample problems and sample tests with an open mind.
