It is know that a certain piece of city-owned land is in a 50 year flood plain,

Question

It is know that a certain piece of city-owned land is in a 50 year flood plain, i.e. during a 50 year period you can expect one flood. Suppose that the city erects a building on this site. Use the Poisson distribution to answer the questions. What is the probability that there will be 2 or more floods m the next 50 years? What is the probability that there will be no floods in the next 20 years? Suppose the land was purchased in 2000 and that a flood occurred during 2005. The Mayor then gleefully proclaims that there will be no flood on this property during the next 45 years. What is the probability that there are one or more floods on this property during the next 45 years?

Explanation / Answer

We have a poisson distribution with parameter = mean = =1 P(X = k) = e^(-) * ^k / k! 1) P(X = 2) = e^(-1) * 1^2 / 2! = 1 / (2e) = .1839 2) for 20 years = for 50 years * 20 / 50 = 1 * 20 /50 = 2/5 P(X = 0) = e^(-2/5) * (2/5)^0 / 0! = e^(-2/5) = .6703 3) for 45 years = for 50 years * 45 / 50 = 9/10 =.9 P(X = 0) = e^(-9/10) * (9/10)^0 / 0! = e^(-9/10) = .4066 P(at least 1 flood) = 1 - P(0 floods) = 1 - .4066 = .5934 Note: The mayor is wrong because a poisson process is memoryless,and therefore previous floods have no impact on the probability offuture floods.

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