Question

Suppose the waiting time between earthquakes in B is an exponential random variable. On average, B gets a really bad earthquake every 100 years. Given that the last really bad earthquake was 99 years ago, compute the probability we get a really bad earthquake within one year from now.

Answer is 0.00995

Answer 1

Let X be the time between two earthquakes              
Then, X follows exponential distribution with parameter λ = 1/100 earthquakes per year              
λ = 1/100              
An Exponential distribution is a memory less distribution.              
Thus, the occurrence of an earlier earthquake does not affect the probability of occurrence of the next earthquake              
To find P(next bad earthquake will be in 1 year )              
that is to find, P(X < 1)              
We use Excel function EXPON.DIST to find the probability              
P(X < 1) = EXPON.DIST(1, λ, TRUE)              
   = EXPON.DIST(1, 1/100, TRUE)          
   = 0.00995          

P(next bad earthquake will be in 1 year ) =    

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