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The phrase 'same distribution with' is correct and usable in written English.
You can use it to indicate that something is distributed in the same way as something else. For example, "The new retail center has the same distribution with the old one, with stores arranged in concentric circles."
Exact(22)
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. .
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 +.
If the random variables T and Y have the same distribution with the same parameters, then G = F.
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.
Similar(38)
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).
The pressure and the voltage appear to follow the same distribution pattern with the highest values being at the injection well, as expected.
We assume that single excisions with unknown length have the same distribution as those with known length in the same age group.
In HEK293T cells transfected with this plasmid the localization of CFP was unequivocally nuclear, with sub-localization to the nucleoli, and the same distribution was seen with CFP fused to full-length Sdf-1γ (pCFPSdf1γ−96−450) (Fig. 2C).
He cited an example where a "perfectly legitimate" email related to the G20 summit was sent to the Treasury and some other international partners – and then appeared again within minutes, sent to the same distribution list but with the attachment on the email swapped to one that contained malicious code that could infect machines running Windows.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com