This elementary example illustrates the above definition of multidimensional probability density functions in the simple case of a function of a set of two variables. Let us call R → → a 2-dimensional random vector of coordinates (X, Y) : the probability to obtain R → → in the quarter plane of positive x and y is Pr ( X > 0 , Y > 0 ) = ∫ ∫ 0 ∞ ∞ ∫ ∫ 0 ∞ ∞ f X , Y ( x , y ) d x d y .