2019 july question 1 a the occurrence of earthquakes is commonly model

Question

2019 July
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.