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Let X M and Y M be two scalar random variables, with vary such that (text {var}(X_{M} =mathcal {O}left (M^{-2}right)) and (text {var}(X_{M} =mathcal {O}left (M^{-2}right)=mathcal {O}left (K^{-2}right)).
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However, these dependence measures can only measure the dependence between two scalar random variables.
However, since in practical situations systems are more complex, the parameters of interest are no longer scalar random variables and they need to be represented by random matrices.
where Y n is a scalar random variable, X n is a vector of random variables, θ are the unknown parameters of interest, and V n is a random variable of the errors.
Since, in general, we have a situation where more complex systems are involved, the parameters of interest are no longer scalar random variables but random vectors and random matrices.
where x and y are two non-negative scalars.
The model underlying our investigations is the correlated scalar random field given by Here, β is an unknown vector of parameters in, a known function and the random term ε(x) has zero mean, (unknown) variance σ and a parameterized correlation structure such that E[ ε(x) ε(x′)] = σ c x, x′; ν) with ν some unknown parameters.
Because the Higgs field is scalar, the spin of the SM Higgs boson is predicted to be zero.
The random parameters in these problems are no longer scalar random variables but potentially vectors and matrices.
Both are defined with two scalar parameters ; λ is the scale parameter and β is the shape parameter.
In Figure 3, there are six camera sensors and four scalar sensors (black solid points).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com