Question

5. Suppose that every three months, on average, an earthquake occurs in a certain region. Assuming this is a Poisson process, what is the probability that the next earthquake occurs after three but before seven months?

Answer 1

Answer:

0.2709

Explanation:

Given that 1 earthquake occurs in 3 months

∴Number of earthquake that will occur in 1 month = 1 / 3

∴ The waiting time of the earthquake to occur can be shown as

$X\sim exp(\frac{1}{3})$

And since it is a poisson distribution as mentioned, the waiting time is always exponential.

Now the probability of the next earthquake that will occur after three but before seven months is

$P(3<X<7)=\int_{3}^{7}(\frac{1}{3})e^{-\frac{x}{3}}.dx$

                     = $e^{-\frac{3}{3}}-e^{-\frac{7}{3}}$

                     = 0.2709

∴ The probability of ht waiting time is 0.2709