Data collected at Toronto Pearson International Airport suggests that an exponential distribution with mean value 2725hours 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 theprobability that it is less than the mean value by more than one standard deviation?

a) What is the probability that the duration of a particular rainfall event at this location is at least 2 hours?

We want this probability"

At most 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?

Step-by-step explanation:

Previous concepts

The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution". The probability density function is given by:

The cumulative distribution for this function is given by:

We know the value for the mean on this case we have that :

Solution to the problem

Part a

What is the probability that the duration of a particular rainfall event at this location is at least 2 hours?

We want this probability"

At most 3 hours?

Part b

What is the probability that rainfall duration exceeds the mean value by more than 2 standard deviations?

The variance for the esponential distribution is given by:

And the deviation would be:

And the mean is given by

Two deviations correspond to 5.540, so we want this probability:

What is the probability that it is less than the mean value by more than one standard deviation?

For this case we want this probablity:

abde or 1,2,4, 5 is the answer

step-by-step explanation: