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Solved: Data collected at Toronto Pearson International
Chapter 4, Problem 61E(choose chapter or problem)
Problem 61E
Data collected at Toronto Pearson International Airport suggests that an exponential distribution with mean value 2.725 hours is a good model for rainfall duration (Urban Stormwater Management Planning with Analytical Probabilistic Models, 2000, p. 69).
a. What is the probability that the duration of a particular rainfall event at this location is at least 2 hours? At most 3 hours? Between 2 and 3 hours?
b. What is the probability that rainfall duration exceeds the mean value by more than 2 standard deviations? What is the probability that it is less than the mean value by more than one standard deviation?
Questions & Answers
QUESTION:
Problem 61E
Data collected at Toronto Pearson International Airport suggests that an exponential distribution with mean value 2.725 hours is a good model for rainfall duration (Urban Stormwater Management Planning with Analytical Probabilistic Models, 2000, p. 69).
a. What is the probability that the duration of a particular rainfall event at this location is at least 2 hours? At most 3 hours? Between 2 and 3 hours?
b. What is the probability that rainfall duration exceeds the mean value by more than 2 standard deviations? What is the probability that it is less than the mean value by more than one standard deviation?
ANSWER:
Answer
Step 1 of 6
Given mean=2.725
1/=2.725
The pmf of exponential distribution is
p(x)=, x
0
The Cdf of exponential distribution is
F(x)=1-