© 2016 Microsoft Corporation. All Rights Reserved.
Page 1
3/3/2017
Chapter 69
The Poisson and exponential
random variable
Questions answered in this chapter:
•What is the Poisson random variable? •How do I compute probabilities for the Poisson random variable? •If the number of customers arriving at a bank is governed by a Poisson random variable, what random variable governs the time between arrivals?
Answers to this chapter’s questions
What is the Poisson random variable? The Poisson random variableis a discrete random variable that is useful for describing probabilities for situations in which events (such as customer arrivals at a bank or orders placed for a product) have a small probability of occurring during a short time interval. More specifically, during a short time interval, denoted as t, either zero or one event will occur, and the probability of one event occurring during a short interval of length tis (for some λ) given by λt. Here, λ(lambda) is the mean number of occurrences per time unit. Situations in which the Poisson random variable can be applied include the following: •Number of units of a product demanded during a month. •Number of deaths per year by horse kick in the Prussian army. •Number of car accidents you have during a year. •Number of copies of The Seat of the Soulordered today at Amazon.com. •Number of workers’ compensation claims filed at a company this month.•Number of defects in 100 yards of string. (Here, 1 yard of string plays the role of time.) How do I compute probabilities for the Poisson random variable? You can use the Microsoft Excel 2016 POISSON.DIST function to compute probabilities involving the