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Joint probability distribution
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===Joint distribution for independent variables=== In general two random variables <math>X</math> and <math>Y</math> are [[statistical independence|independent]] if and only if the joint cumulative distribution function satisfies :<math> F_{X,Y}(x,y) = F_X(x) \cdot F_Y(y) </math> Two discrete random variables <math>X</math> and <math>Y</math> are independent if and only if the joint probability mass function satisfies :<math> P(X = x \ \mbox{and} \ Y = y ) = P( X = x) \cdot P( Y = y) </math> for all <math>x</math> and <math>y</math>. While the number of independent random events grows, the related joint probability value decreases rapidly to zero, according to a negative exponential law. Similarly, two absolutely continuous random variables are independent if and only if :<math> f_{X,Y}(x,y) = f_X(x) \cdot f_Y(y) </math> for all <math>x</math> and <math>y</math>. This means that acquiring any information about the value of one or more of the random variables leads to a conditional distribution of any other variable that is identical to its unconditional (marginal) distribution; thus no variable provides any information about any other variable.
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