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where P denotes probability and P[a|b] denotes probability of a conditioned on b.
p(a|b) denotes the probability density function (pdf) of random variable a conditioned on b, Pr represents the probability of a variable.
The a posteriori probability that the information symbol ξ equals a conditioned on the length- N b (=N p) received bit sequence r 1 N b = ( r 1, r 2, …, r N b − 1, r N b ) is P ξ = a | r 1 N b = P ξ = a, r 1 N b P r 1 N b = 1 P r 1 N b ∑ ζ ∑ ζ ′ P ξ = a, ζ τ = ζ, ζ τ − p = ζ ′, r 1 N b (2).
Similar(57)
This allowed him to grant lands to his nobles as a privilege, conditioned on their military support.
On Friday, Constellation had made an offer of $35, conditioned on an examination of Vincor's books.
The Bank said its view was conditioned on a "smooth" Brexit process.
They will never wonder whether their father's love is conditioned on an unblemished report card.
Then, conditioned on follows a Gaussian distribution [21]: (3).
Conditioned on, is a complex Gaussian random variable.
It is a condition on telling a lie that one makes an assertion.
Monotonicity is a condition on every pair of values, whereas cyclic monotonicity is a condition on every finite sequence of values.
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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