questions about using the exponential distribution

Question

i can't seem to find any good examples i can adapt to solve this problem.

a certain place experiences an earthquake once every 10 years.

what's the probability that there will be an earthquake within the next 5 years? 20 years? i have to use the exponential distribution.

i think i am supposed to look at this problem in terms of 1 year, so the probability that there will be an earthquake in any particular year is

$\mu = \frac{1}{10}$.

i also think this implies that the probability of an earthquake within the next five years is

$\mu = \frac{1}{20}$

because this period is half as long as the above one.

for 20 years, i think it's

$\mu = \frac{1}{5}$

because this period is twice as long as the first period.

am i right about all of this?

and to calculate the probability of an earthquake within these periods, would i just calculate a left tail probability using the cumulative exponential distribution?

thanks in advance for any insight.

Answer 1

Exponential distribution works.

$$P(X\leq 5)=1-e^{-\frac{5}{10}}=1-\frac{1}{\sqrt{e}}\approx 39.35\%$$

and so on...

poisson distribution properly set will work too

I suggest you to use Poisson to get the same result