Question

Give an example, USING YOUR OWN WORDS (NOT TEXT COPIED FROM THE INTERNET), of how either the Poisson or the Exponential distribution could be used to model something in real life (only one example is necessary). You can give an example in an area that interests you (a list of ideas is below). Give a very rough description of the sample space.

If you use an idea from another source, please provide a citation in the sentence and a reference entry at the end of your post. Include a citation even if you paraphrase from a website. Please do not copy blocks of text from the Internet--try to use your own words.

When forming your answer to this question you may give an example of a situation from your own field of interest for which a random variable, possibly from one of the types that are presented in this unit, can serve as a model. Discuss the importance (or lack thereof) of having a theoretical model for the situation. People can use models to predict business conditions, network traffic levels, sales, number of customers per day, rainfall, temperature, crime rates, or other such things.

Answer 1

Suppose you are a manager of a recreational park. You saw that the ticket que lines are hapazard and inefficient. now you want to model the flow of people into the park

>> First you want to know the arrival rate of people and its probabiity.

>> Let X be the number of arrival per hour. X follows a poissin distribution. The arrival of people tells you how many ticket both is required to maintain short waiting time for customer which will increses the satisfaction level

>>Let Y be the interarrival time between two people in the ques. This interarrival time is exponentially distrbuted.

>> Suppose you want to know the service rate. Let Z be time to book one ticket by ticket server. Then Z also follows exponential distribution.

NOTE: all the notes above is fictional and not copied or referred to any other sources.