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The null hypothesis of ωpop and ωML being independent random samples from the same distributions with equal means and equal but unknown variances is strongly rejected when Δ G greater than − 6 kcal/mol (supplementary fig. S3, Supplementary Material online).

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The down-regulated genes have the same distribution, with the exception of the cytosol.

(b) If the random variables T and Y have the same distribution with the same parameters, then G = F.  .

If the random variables T and Y have the same distribution with the same parameters, then G = F.

First, we show that the accumulated aggregate claim (S_{n}) in (1.1) has the same distribution with another random walk.

Define { χ n + }, n ≥ 2, as the sequence of independent random variables having the same distribution with χ 1 +.

Lemma 1: (a) If the random variables X f and Y have the same distribution with the same parameters, then G = R.

The motivation for using skewed Normal rather than Weibull distribution is to facilitate a better comparison across different scenarios using the same distribution with different parameters.

z ̃ k has the same distribution with z k, because the pdf of z k in (42) has nothing to do with ϕ m, ϕ n.

Recalling that the one-time-slot infection process has the same distribution with the virtual source branching process, we obtain ρ v ≤ ρ v ( mi ), ∀ v.

By observing that (theta ^{-1/d} mathcal {P}(lambda)) has the same distribution with (mathcal {P}(lambda theta)), we obtain the scaling property of (hat beta _{k}(lambda, r)).

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