I need help!! Can an awesome genius please help me out?
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Answer:
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:
Solution to the problem
For this case the time between breakdowns representing our random variable T is exponentially distirbuted
So on this case we can find the value of like this:
So then our density function would be given by:
The exponential distribution is useful when we want to describe the waiting time between Poisson occurrences. If we assume that the random variable T represent the waiting time between two consecutive event, we can define the probability that 0 events occurs between the start and a time t, like this:
And on this case we are looking for this probability: