A new approach on the renewal process with Geometric interarrival times

ABSTRACT: This paper develops the probability of a renewal process, whose interarrival are independent and identically distributed (i.i.d.) random variables (R.V.s) with geometric distribution. The distribution of the number of renewals in (0,t] and the joint distribution of the number of renewals in (0,a] and [a,b], 0 < a < b, are obtained. Then, using the joint distribution, the distribution of the number of renewals in [a,b], 0 < a < b, is obtained. Finally, we show that every renewal processes, whose interarrivals are i.i.d. discrete R.V.s, has independent and stationary increment if and only if its interarrivals be geometric distribution.