Data collected at Toronto Pearson International Airport suggest that an exponential distribution with mean value 2,725 hours is a good model for rainfall duration. What is the probability that the duration of a particular rainfall event at this location is at least 2 hours?

And we can calculate this with the complement rule like this:

And using the cdf we got:

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:

And 0 for other case. Let X the random variable of interest:

Solution to the problem

We want to calculate this probability:

And we can calculate this with the complement rule like this:

And using the cdf we got:

(x+3)(x+7)

step-by-step explanation: