Thus given the arrival times denoted by have the same distribution as the order statistics corresponding to independent random variables uniformly distributed in the interval .
Proof of property 2
Let and also assume are small increments of time such that , . This concept is explained in the following Figure 2.7.
Figure 2.7: Concept of conditional distribution of arrival times
the 
arrival times denoted by 
have the same distribution as the order statistics corresponding to 
independent random variables uniformly distributed in the interval 
.
and also assume 
are small increments of time such that 
, 
. This concept is explained in the following Figure 2.7.
