Editing Independence (probability theory) (section)

====For two stochastic processes====
Independence of two stochastic processes is a property between two stochastic processes <math>\left\{ X_t \right\}_{t\in\mathcal{T}}</math> and <math>\left\{ Y_t \right\}_{t\in\mathcal{T}}</math> that are defined on the same probability space <math>(\Omega,\mathcal{F},P)</math>. Formally, two stochastic processes <math>\left\{ X_t \right\}_{t\in\mathcal{T}}</math> and <math>\left\{ Y_t \right\}_{t\in\mathcal{T}}</math> are said to be independent if for all <math>n\in \mathbb{N}</math> and for all <math>t_1,\ldots,t_n\in\mathcal{T}</math>, the random vectors <math>(X(t_1),\ldots,X(t_n))</math> and <math>(Y(t_1),\ldots,Y(t_n))</math> are independent,<ref name="Lapidoth2017">{{cite book|author=Amos Lapidoth|title=A Foundation in Digital Communication|url=https://books.google.com/books?id=6oTuDQAAQBAJ&q=independence|date=8 February 2017|publisher=Cambridge University Press|isbn=978-1-107-17732-1}}</ref>{{rp|p. 515}} i.e. if

{{Equation box 1
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|equation = {{NumBlk||<math>F_{X_{t_1},\ldots,X_{t_n},Y_{t_1},\ldots,Y_{t_n}}(x_1,\ldots,x_n,y_1,\ldots,y_n) = F_{X_{t_1},\ldots,X_{t_n}}(x_1,\ldots,x_n) \cdot F_{Y_{t_1},\ldots,Y_{t_n}}(y_1,\ldots,y_n) \quad \text{for all } x_1,\ldots,x_n</math>|{{EquationRef|Eq.8}}}}
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