MAT 316 Lecture Notes - Lecture 11: Memorylessness, Unimodality, Queueing Theory
Document Summary
Recall that the names of continuous distributions refer to shapes. The exponential distribution starts high and drops continuously as x increases. In the formula for the density the starting point is at 0, although it can easily be shifted to start at any real number. While the exponential distribution has many real-world applications, there are two in particular where the exponential is used extensively. One, which is used in a reliability setting, is that it models the lifetimes of electronic components. The other, which is used in operations research, is that it models the time between poisson occurrences. Depending on which of these two applications is most prevalent in a particular book, the density for the exponential can be written two different ways. The two are equivalent; the difference is merely notational. Note that these are exactly the same thing, where the in the exponential 1 is replaced with in the exponential 2.
