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Let (X,Y) be a pair of random variables with supp(X)⊆[0,1] and EY2<∞.
Then, the probability distribution of a pair of random variables (59).
Theorem 2.4 Let ( A, B ) be a pair of random variables with B > 0 in the probability space ( Ω, F, P ) satisfying the canonical assumption.
A pair of random variables ( X, Y ) is positively quadrant dependent if P { X ≤ x, Y ≤ y } ≥ P { X ≤ x } P { Y ≤ y }, x, y ∈ R. (1).
Let ( A, B ) be a pair of random variables with B > 0 in the probability space ( Ω, F, P ) satisfying the canonical assumption.
This paper investigates the lateral vibration of a spinning disk shaft system supported by a pair of ball bearings and subjected to a pair of random axial forces at both ends.
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In short, we wanted to turn the universe into a pair of random-number generators.
For a pair of NSD random variables X, Y, by the property (a) in Lemma 1, we have H x,y)=P Xleq x,Yleq y -P Xleq x)P(y -P Xleqq0.
In Figure 2, correlated information sequences a T and b T are generated by repeated independent drawings of a pair of discrete random variables, where a T = [a 1,a 2,…,a L ]= {a i }, b T = [b 1,b 2,…,b L ]= {b i }, a i ∈ {1,2,…,A}, b i ∈ {1,2,…,B}, i∈{1,2,…,L}, and L is the total number of drawings.
According to entropy theory, assume X and Y are a pair of discrete random variable where X, Y~P x, y), the joint entropy of X and Y defined as H X, Y = − ∑ x ∈ X ∑ y ∈ Y P x, y log p x, y (19).
Chatroulette does an excellent job of representing the world in its truest form: sometimes you'll meet kindly strangers willing to talk about pancakes - other times you'll simply see a pair of a random strangers' balls.
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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