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An upper bound for the probability for performing less than w successful swaps in T iterations can be calculated by the binomial probability: q le sumlimits_{i = 0}^{w - 1} {left( {begin{array}{*{20}c} T i end{array} } right)} cdot left( {frac{{alpha^{2} }}{{k^{2} }}} right)^{i} cdot left( {1 - frac{{alpha^{2} }}{{k^{2} }}} right)^{T - i} (13).
The probability of observing n orthologue pairs in which both genes are HI, out of N pairs tested, is then given by the binomial probability of n successes, and (N-n) failures, with probability of success = 0.2.
Each state is defined in the HMM by the binomial probability of observing the number of reads aligned to each base from the infected sample, given the total number of reads that align to each base; because the number of reads that map from the infected and naïve samples is not equal, the binomial probably for the unregulated class is not expected to be 0.50 (Table 1; see Methods for details).
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In order to reduce the influence of missing data, we excluded pathways whose members were not significantly detected by GPL96 platform by using the binomial probability model.
To determine what significance there was to the genomic arrangement that we found, we calculated the statistical significance of this arrangement by using the binomial probability.
For a gene to be considered up-regulated by σB, the binomial probability of observing as many reads in the Δ sigB strain as those observed for 10403S had to be < 0.05 for each of the four possible combinations.
Conversely, for a gene to be considered down-regulated by σB, the binomial probability of observing as many reads as those observed for Δ sigB had to have q-values < 0.05 for each of the four possible combinations.
We denote by the estimate of the binomial probability parameter learned from the count data generated with BARD-C simulator.
95% confidence intervals (CI) on the binomial probability were calculated by the Wilson method.
We can only compute this probability for a blind attacker, who generates the vector by flipping a fair coin, which results in the binomial probability distribution over passwords.
Here, the binomial probability for each was given by the observed SAR and the number of trials was the number of ferrets used.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com