During the years 1998–2012, a total of 29 earthquakes of magnitude greater than
ID: 3042974 • Letter: D
Question
During the years 1998–2012, a total of 29 earthquakes of magnitude greater than 6.5 have occurred in Papua New Guinea. Assume that the time spent waiting between earthquakes is exponential.
a)What is the probability that the next earthquake occurs within the next three months?
b)Given that six months has passed without an earthquake in Papua New Guinea, what is the probability that the next three months will be free of earthquakes?
c)What is the probability of zero earthquakes occurring in 2014?
d)What is the probability that at least two earthquakes will occur in 2014?
Explanation / Answer
total months = 12 *14 = 168
rate = 29/168 = (1/ 5.79310) earthquake /month
a) P(X <= 3) = 1 - e^(- 1/ 5.79310*3)
= 0.4042042
b)
exponential distribution have memoryless property
hence
P(X > 3) = 1 - P(X< 3) = 0.59579
c)
there are 12 months in a year
hence
P(X > 12) = e^(- 1/ 5.79310*12) = 0.126
d)
number of earthquake is poisson distribution with mean = (1/ 5.79310) earthquake /month
hence for one year
rate = 29/14 = 2.0714285
hence
P(X>=2) = 1 - P(X = 0) - P(X = 1)
= 0.61298
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