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Climate change has increased the frequency and intensity of rainstorms in many parts of the world, and accurate modeling of those storms is critical to reduce the chance of flooding. The article "Bivariate Frequency Analysis of Rainfall Intensity and Duration for Urban Stormwater Infrastructure Design" (J. Hydrol., 2017: 374-383) indicates that a Poisson process provides a good model for the number of rainfall events in a given region. The rate parameter λ depends on the specific region and the intensity threshold (mm. hr-¹) of the events being counted; for instance, the authors modeled the number of rainstorms with intensity of at least 5 mm hr-¹ in a certain region of Singapore via a Poisson process with λ = 4.8 per year. a. What is the probability of at least six such rainstorms in one year? At least 10? b. What is the probability that the number of such rainstorms in a three-year period will exceed its expected value by more than one standard deviation? c. For what duration of time would the probability of at least one such rainstorm be .999?

Climate change has increased the frequency and intensity of rainstorms in many parts of the world, and accurate modeling of those storms is critical to reduce the chance of flooding. The article "Bivariate Frequency Analysis of Rainfall Intensity and Duration for Urban Stormwater Infrastructure Design" (J. Hydrol., 2017: 374-383) indicates that a Poisson process provides a good model for the number of rainfall events in a given region. The rate parameter λ depends on the specific region and the intensity threshold (mm. hr-¹) of the events being counted; for instance, the authors modeled the number of rainstorms with intensity of at least 5 mm hr-¹ in a certain region of Singapore via a Poisson process with λ = 4.8 per year. a. What is the probability of at least six such rainstorms in one year? At least 10? b. What is the probability that the number of such rainstorms in a three-year period will exceed its expected value by more than one standard deviation? c. For what duration of time would the probability of at least one such rainstorm be .999?

MATLAB: An Introduction with Applications
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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Climate change has increased the frequency and intensity of rainstorms in many parts of the world, and accurate modeling of those storms is critical to reduce the chance of flooding. The article "Bivariate Frequency Analysis of Rainfall Intensity and Duration for Urban Stormwater Infrastructure Design” (J. Hydrol., 2017: 374-383) indicates that a Poisson process provides a good model for the number of rainfall events in a given region. The rate parameter λ depends on the specific region and the intensity threshold (mm · hr¯¹) of the events being counted; for instance, the authors modeled the number of rainstorms with intensity of at least 5 mm · hr¯¹ in a certain region of Singapore via a Poisson process with λ = 4.8 per year. a. What is the probability of at least six such rainstorms in one year? At least 10? b. What is the probability that the number of such rainstorms in a three-year period will exceed its expected value by more than one standard deviation? c. For what duration of time would the probability of at least one such rainstorm be .999?
Transcribed Image Text:Climate change has increased the frequency and intensity of rainstorms in many parts of the world, and accurate modeling of those storms is critical to reduce the chance of flooding. The article "Bivariate Frequency Analysis of Rainfall Intensity and Duration for Urban Stormwater Infrastructure Design” (J. Hydrol., 2017: 374-383) indicates that a Poisson process provides a good model for the number of rainfall events in a given region. The rate parameter λ depends on the specific region and the intensity threshold (mm · hr¯¹) of the events being counted; for instance, the authors modeled the number of rainstorms with intensity of at least 5 mm · hr¯¹ in a certain region of Singapore via a Poisson process with λ = 4.8 per year. a. What is the probability of at least six such rainstorms in one year? At least 10? b. What is the probability that the number of such rainstorms in a three-year period will exceed its expected value by more than one standard deviation? c. For what duration of time would the probability of at least one such rainstorm be .999?
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