It is supposed that the densities of two components, the dark matter and the dark energy, dominate the total energy density of the universe [1, 2, 3, 4].
Also, we suppose that the density function is almost everywhere continuous with respect to λ.
For that, it is supposed that the probability density function associated to Y on the sample points s 1, s 2,…, s n is a multidimensional Gaussian: frac{1}{{left(2pi right)}^{frac{n}{2}} det {(K)}^{frac{1}{2}}{ee}^{-frac{1}{2}{left Z-Fbeta right)}^T{K}^{-1}left Z-Fbeta righT{K}^{-1}left Z-Fbeta
For this, suppose that the probability density functions of all components of the stochastic vectors and, of the matrices and are normally distributed.
Rename ' t n ' to 't' and suppose that the particular density functions can be expressed in powers of parameter h by the Taylor formula.
Suppose that the conditional density of a response variable given a vector of explanatory variables is parametrically modelled, and that data are collected by a two-phase sampling design.
Furthermore, suppose that the probability density functions of all components of the stochastic vector are normally distributed, and are statistically independent, then, the model (2.5) can be equivalently written as: (2.6).
Let Y n denote some arbitrary continuous random variable and suppose that the probability density of Y n evaluated at y n is the function f n (y n ).
They also supposed that the sequence ({Y_{n},ngeq 1}) is bounded, as well as the density (f(x)) of (X_{1}).
Schrödinger originally supposed that the electron was spread out in space and that its density at point x, y, z was given by the value of Ψ2 at that point.
We suppose that the absolute densities of olivine and inert components are constant.
