Definition :
Definition :
Formula :The formula for calculating probabilities using the Poisson distribution is
where
is the average number of occurrences in the specified interval. For the Poisson distribution,
Illustration :
EX. The number of false fire alarms in a suburb of Houston averages 2.1 per day. Assuming that a Poisson distribution is appropriate, the probability that 4 false alarms will occur on a given day is given by
Ex. On an average Friday, a waitress gets no tip from 5 customers. Find the probability that she will get no tip from 7 customers this Friday.
The waitress averages 5 customers that leave no tip on Fridays : λ = 5.Random Variable : The number of customers that leave her no tip this Friday.
We are interested in P (X = 7)
So, the probability that 7 customers will leave no tip this Friday is 0.1044.
Ex. During a typical football game, a coach can expect 3.2 injuries. Find the probability that the team will have at most 1 injury in this game.A coach can expect 3.2 injuries : λ = 3.2.
Random Variable : The number of injuries the team has in this game.
We are interested in P (X<=1).
Application :
The Poisson distribution is most commonly used to model the number of random occurrences of some phenomenon in a specified unit of space or time. For example,
The number of phone calls received by a telephone operator in a 10-minute period. The number of flaws in a bolt of fabric. The number of typos per page made by a secretary.
Applet :
See an illustration of the Poisson distribution http://www.capdm.com/demos/software/html/CAPDM/qm/poissondist/usage.html
References :
The above materials taken from http://infinity.sequoias.cc.ca.us/faculty/woodbury/Stats/Tutorial/Pois_Form.htm and
http://stat.tamu.edu/stat30x/notes/node70.htm
A little about the mathematician himself - http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Poisson.html
