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Question 1

(a)

The occurrence of earthquakes is commonly modelled by a Poisson process.

Assume that the occurrence of an earthquake in a certain region was modelled by

a Poisson process with an annual rate of 0.01.

Analyze and compute the probability of occurrence of exactly one

earthquake in 1 year.

(iv) Analyze and compute the probability of occurrence of one or more

earthquake in 1 year.

Analyze and compute the probability of occurrence of two earthquakes in

2 years.

(iii) Analyze and compute the probability of having an earthquake

time more than 100 years after the last occurrence.