Question

For a recent period of 100 years, there were 86 major earthquakes in a particular region. Assuming that the Poisson distribution is a suitable model, find the mean number of major earthquakes per year. mean - Now, find the probablity distribution for the number of earthquakes in a randomly selected year: 6 or more

Answer 1

This is a question of poisson distribution with

Mean =86/100= 0.86

For a Poisson Distribution

P(X = x) - ehrl P(X = 0) 0-0.560.86

P(X = 0) = 0.4232

21 b)x=1 e-0.86 0.861 P(X = 1)=2 P(X = 1) = 0.3639 c).x = 2 e-0.86 0.862 P(X = 2) = 9 P(X = 2) = 0.1565 d).x = 3 e-0.86 0.863 P(X = 3) = ? P(X = 3) = 0.0449 e).r = 4 e-0.86 0.864 P(X = 4) = P(X = 4) = 0.0096 fr = 5 P(X = 5) = .0.865 5! P(X = 5) = 0.0017 g).x = 6 P(X > 6) = 1- P(X<6) P(X > 6) = 1- P(X = 0) – P(X = 1) - P(X = 2) – P(X = 3) - P(X= 4) - P(X = 5) e-0.86 e-0.86 P(X > 6) = 1-9 - 3 .8622! - S .8633! 0 9 .8644! - 4.8695! P(X>6) = 1 – 0.4232 – 0.3639 – 0.1565 – 0.0449 – 0.0096 – 0.0017 P(X > 6) = 0.0005 e-0.86 86'0! -0.86 86111 0 e-0.86 -0.86 0 0 .8644 0

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