Consider a Poisson process with intensity 2 and a union of t

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:

(a) There are at least two arrivals in I.

(b) There are precisely three arrivals in I.

(c) There are at most four arrivals in I.

Solution

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 e

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