Batch Renewals. Consider times , where the ξk are i.i.d. with distribution F and F(0) = P{ξk = 0} > 0. The associated point process N(t) is a renewal process with instantaneous renewals (or batch...

Batch Renewals. Consider times
, where the ξk are i.i.d. with distribution F and F(0) = P{ξk = 0} > 0. The associated point process N(t) is a renewal process with instantaneous renewals (or batch renewals). In the notation of Exercise 20,
 (Tˆn ≤ t), where νn is the number of renewals exactly at time Tˆn. Specify the distribution of νn. Are the νn i.i.d.? Are they independent of Tˆn? Specify the distribution of Tˆ
¹
in terms of F. Exercise 20