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when given an interval of real number, assume events occur at random throughout the interval. If the interval can be partitioned into subintervals of small enough length such that

1. the probability of more than 1 event in a subinterval is 0

2. thw probability of one events in a subinterval is the same for all subintervals and proportional to the length of the subinterval, and

3. the event in each interval is indepedent of other subintervals, the random experiment is called " POISSON process". "

But i don't really understand what is it mean for part 1.

Can any one explain to me?

thx..