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Data collected on volcanic eruptions give a mean time between eruptions of 29 months. Assume these eruptions occur as a Poisson process in time, find the:

(a) Expected number of eruptions during the five-year period beginning from the time you have read this question.

(b) Probability that there will be exactly two eruptions during this five-year period.

(c) Probability that at least three years will pass from now before the next erupt

(d) Probability that the waiting time between two consecutive earthquakes exceeds two year