 Let G be the average number of nodes that begin transmission within period T (the frame time).If a large number of nodes is trying to transmit, then by using Poisson distribution, the probability that exactly x nodes begin transmission during period T is

formula_7

Therefore, the probability that during any particular period from t=2nT to t=(2n+1)T, (that is for any particular non-zero integer value of n) exactly one node will begin transmission is

formula_8

And the probability that during any particular period t=(2n+1)T to t=(2n+2)T, no node will begin transmission is

formula_9

But for successful transmission of a frame, both the events should occur simultaneously.That is during period t=2nT to t=(2n+1)T, exactly one node begins transmission and during t=(2n+1)T to t=(2n+2)T no node begins transmission.