For another approach to proving that Definition 2.1.2 implies Defini- tion 2.1.1.

(a) Prove, using Definition 2.1.2, that Po(ts) Po(t) Po(s)

(b) Use

(a) to infer that the interarrival times X1, X2,... are independent exponential random variables with rate A.

(c) Use

(b) to show that N(t) is Poisson distributed with mean At.