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

0.2709

Step-by-step 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((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)((1)/(3))e^{-(x)/(3)}.dx`

=
`e^{-(3)/(3)}-e^{-(7)/(3)}`

= 0.2709

∴ The probability of ht waiting time is 0.2709