Consider a Poisson process with intensity 2 and a union of two disjoint time intervals I = [3, 4] [6, 8] . Give formulas for the probabilities of the following events:

1 There are at least two arrivals in I.

2 There are precisely three arrivals in I.

3 There are at most four arrivals in I.

hint:

We can treat I as if it were an interval, because increments are both stationary and independent. What matters is the total length of Z, which is 3. The d length t when is the intensity, is as follows: of the number of arrivals, in a ti me interval of Pr(N(t) = k) = e-At(At)" k! We can treat I as if it were an interval, because increments are both stationary and independent. What matters is the total length of Z, which is 3. The d length t when is the intensity, is as follows: of the number of arrivals, in a ti me interval of Pr(N(t) = k) = e-At(At)" k