5. In a country, which is the target of more natural disasters than most other countries, the time between two consecutive natural disasters is a gamma random variable with parameters r = 3 and λ = 2, independently of the times of the occurrences of other natural disasters in that country. Label the time point at which a natural disaster occurs as t = 0. Let X1, X1 +X2, X1 +X2 +X3, . . . , be the times of the occurrences of the subsequent disasters, respectively. Define and find the long-term rate at which natural disasters occur in this country.

Hint: Argue that the rate at which natural disasters occur should be defined by

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