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PLEASE USE R FOR THE FOLLOWING ANSWERS TO THE NEAREST 0.0001 ACCURACY! THANK YOU :-) Data...

PLEASE USE R FOR THE FOLLOWING ANSWERS TO THE NEAREST 0.0001 ACCURACY!

THANK YOU :-)

Data collected at Hancock Airport in Syracuse NY
suggests that an exponential distribution with mean value
3.2 hours is a good model for rainfall duration (Urban
Stormwater Management Planning with Analytical
Probabilistic Models, 2000, p. 69). (Keep in mind that the mean is μ = 1/λ)


a. What is the probability that the duration of a partic-
ular 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?

c. The duration of a rainfall event hits 3 hours. At that precise time, you know – are given –
that the duration is at least 3 hours. What is the conditional probability the duration will
be at least 5 hours? (That’s an additional 2 hours. Compare the answer to that of the first
part of part a.)


d. The rainfall is given to have lasted less than 5 hours. What is the conditional probability
it lasted less than 3 hours?

math   Statistics-And-Probability   
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