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Poisson and Binomial Distribution question?
Suppose that the number of devastating earthquakes (above a certain magnitude and occurring in a populated region and/or producing dangerous tsunami) occurring somewhere in the world averages out to 2.5 per year. Furthermore, assume that the occurrence of devastating earthquakes is a Poisson process.
Over any given 10-year period, what is the probability that there will be 3 or more years in which 1 or fewer earthquakes happen in each of those years?
1 Answer
- 1 decade agoFavorite Answer
for possion distribution P(k)=(e^-2.5)*(2.5^k)/k!;
P(1 or fewer earthquakes happen in one year)
=P0+P1
=0.2873
for 3 or more years in which 1 or fewer earthquakes happen in each of those years in 10-year period,
it is a binomial distribution with p=0.2873 and q=1-0.2873=0.7127 and n=10
1 - C(10,0)p^0*q^10 + C(10,1)p^1*q^9 + C(10,2)p^2*q^8
=0.5826
