On the event distance of Poisson processes with applications to sensors
We derive a closed formula for the expected distance between Poisson events of two i.i.d. Poisson processes with arrival rate ? ? and respective arrival times X1,X2, X 1 , X 2 ,  and Y1,Y2, Y 1 , Y 2 ,  Namely, for any integers r?0,k?1 r ? 0 , k ? 1 , the following identity holds:
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