
Aims and Objectives: Provide a further opportunity (extending the work carried out on the previous parcatical  Practical 5) for students to apply their knowledge of loops (pretest and posttest, and fixed and variable count) using the "for", "while" and/or "dowhile" loop constructs taught in weeks 7 and 8.
Given knowledge of the averrage (A) arrival rate of customers at some business (e.g. bank, post office, shop, etc.) the likelyhood of a particular number of customers (X) arriving can be estimated using the Poisson probability function (named after Siméon Denis Poisson): where X is a number of customer arrivals per minute, A is the average number of arrivals per minute, X! is factorial(X), and e is Euler's number (2.7182818). For example if A = 3 then the probability of one customer entering the premises is: Develop a Java software system which takes as input a usersupplied average arrival rate (A), and calculates and displays the Poisson probability associated with a range of values for X (numbers of customers arriving) according to the following:


Assume that A is an integer between 1 and 10.
EXAMPLE 1: Given A=9 (thus A5 > 0) then the output would be on the following lines: Number of  Poisson Customers  Probability (X)  + 4  0.033737 5  0.060727 6  0.091091 7  0.117117 8  0.131756 9  0.131756 10  0.118581 11  0.097021 12  0.072765 13  0.050376 14  0.032384 
EXAMPLE 2: Given A=2 (thus A5 <= 0) the output will be of the form: Number of  Poisson Customers  Probability (X)  + 1  0.270671 2  0.270671 3  0.180447 4  0.090224 5  0.036089 6  0.012030 7  0.003437 
Note 1: You should build at least two classes, one that characterises the "Poisson probability" problem in general and an application class. Note 2: To calculate a X! (factorial X) make use of the Factorial class presented in lectures (week 7). To use this you will have to copy (cut and past!) the class into the same directory as your other classes used to address this practical. Once compiled you can create intances of the Factorial class which may be of use in the solution to the current problem. (Assume that the Factorial has been properly designed and tested and thuys will not rerquire any further design or testing,) Note 3: Euler's constant can be found in the Math class where it is defined as a class field and can thus be accessed by linking it to the name of the class, Math.E. 
Siméon Denis Poisson (1781  1840) ^{1} 
Your solution should comprise the following:
Your report should comprise the following sections:
All supporting documentation should be prepared as a single Microsoft Word file.
Once completed you should "up load" your Java source files (extension .java) and your word document to the CS department's electronic "practical assignment submission" system.
Marks will be awarded for:
With the total number of available marks distributed as indicated.
Remember:
Created and maintained by Frans Coenen. Last updated 30 October 2006