The number of floods that occur in a certain region over a given year is a random variable having a Poisson distribution with mean 1.8, independently from one year to the other. Moreover, the time period (in days) during which the ground is flooded, at the time of an arbitrary flood, is an exponential random variable with mean 3. We assume that the durations of the floods are independent. Using the central limit theorem, calculate (approximately) (a) the probability that over the course of the next 20 years, there will be at least 19 floods in this region. Assume that we do not need to apply half-unit correction for this question. (b) the probability that the total time during which the ground will be flooded over the course of the next 120 floods will be smaller than 365 days.
The number of floods that occur in a certain region over a given year is a random variable having a Poisson distribution with mean 1.8, independently from one year to the other. Moreover, the time period (in days) during which the ground is flooded, at the time of an arbitrary flood, is an exponential random variable with mean 3. We assume that the durations of the floods are independent. Using the central limit theorem, calculate (approximately) (a) the probability that over the course of the next 20 years, there will be at least 19 floods in this region. Assume that we do not need to apply half-unit correction for this question. (b) the probability that the total time during which the ground will be flooded over the course of the next 120 floods will be smaller than 365 days.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:The number of floods that occur in a certain region over a given year is a random variable having
a Poisson distribution with mean 1.8, independently from one year to the other. Moreover, the time
period (in days) during which the ground is flooded, at the time of an arbitrary flood, is an exponential
random variable with mean 3. We assume that the durations of the floods are independent. Using the
central limit theorem, calculate (approximately)
(a) the probability that over the course of the next 20 years, there will be at least 19 floods in this
region. Assume that we do not need to apply half-unit correction for this question.
(b) the probability that the total time during which the ground will be flooded over the course of the
next 120 floods will be smaller than 365 days.
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