Your Question:

The occurrence of floods in a county follows a Poisson distribution with a return period of 20 years. The damage in each flood is log-normally distributed with a mean of $2 million and a coefficient of variation of 25%. Assume that damage in any one flood is statistically independent of the damage in any other flood. (a) What is the probability of more than two floods occurring in the county during the next 10 years? (b) What is the probability that damage in the next flood will exceed $3 million? (c) What is the probability than none of the floods that could occur in the next 10 years will cause damage exceeding $3 million?

Step By Step Answers with Explanation

(a) The probability of more than two floods occurring in the county during the next 10 years can be calculated using the following steps:

2. Subtract the probability of having two or fewer floods from 1 to get the probability of having more than two floods:

P(k > 2) = 1 - P(k <= 2) = 0.39346934

sigma = 0.25 * mu

2. Calculate the cumulative probability of the damage exceeding $3 million using the lognormal cumulative distribution function (CDF):

Therefore, the probability that damage in the next flood will exceed $3 million is 0.

(c) The probability than none of the floods that could occur in the next 10 years will cause damage exceeding $3 million can be calculated using the following steps:

Therefore, the probability than none of the floods that could occur in the next 10 years will cause damage exceeding $3 million is 1.0.

In conclusion, the answers to your questions are: