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Answer:
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 that represent the random variable of interest and we know that the distribution is given by:
We know the variance on this case given by :
So then the deviation is given by:
And if we solve for we got:
The cumulative distribution function for the exponential distribution is given by:
Solution to the problem
And for this case we want to find this probability:
And using the cdf we got: