Course Name: Stats Primer, Section No: 2, Unit No: 23, Unit type: Document
Hi Girish!
Thanks for going through the primer and sharing your feedback. The main objective for the primer is to give a foundation for upcoming EPAT lectures, where we discuss all the concepts in more detail (including probability distributions). But till then, here is an intuitive understanding of the exponential distribution:
The exponential distribution is used to describe the time between events recurring at random points in time, e.g., the time between failures of electronic equipment or the time between arrivals at a service booth.
It is related to the Poisson distribution, which describes the number of occurrences of an event in a given interval of time. Thus, we can also look at an exponential distribution as the probability distribution of the time between the events in a Poisson process. An important characteristic of the exponential distribution is the “memoryless” property, which means that the future lifetime of a given object has the same distribution, regardless of the time it existed. So for eg. if X is a random variable representing the time between arrivals of customers in a shop, the chance that a new customer arrives remains the same irrespective of when the last customer walked in.
For more detail on the mathematical representation, please refer: https://mathworld.wolfram.com/ExponentialDistribution.html
http://www.math.wm.edu/~leemis/probability/samplepages/page257.pdf