Answer:
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: