1. REQUIREMENTS

The arrival rate of customers at some business (e.g. bank, post office, shop etc) can be estimated using the Poisson probability function:

Poisson(X) = (A^X x e^-A)/X!

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 them the probability of one customer entering the premises is:

Poisson(X=1) = (3^1 x 2.7182818^-3)/1
             = 0.149361

Develop an Ada program which takes as input a user supplied 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:

• If A-5 (the average number of customers arriving -5) is greater than zero a range of A-5 to A+5 incrementing in steps of 1 (e.g. if A = 7, then X = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12).
• Otherwise if A-5 is less than or equal to zero then a range of 1 to A+5 incrementing in steps of 1 (e.g. if A = 3, then X = 1, 2, 3, 4, 5, 6, 7, 8).

EXAMPLE 1: Given A=9 (thus A-5 > 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 1: Given A=2 (thus A-5 <= 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

Assume that A is a positive integer between 1 and 10, and that output should be given accurate to 6 decimal places.

Note 1: The factorial program given in lectures is designed to operate using integers up to a maximum of !12. To solve the above problem you will need a FLOAT version.

Note 2: Euler's constant can be found in the MATH_CONSTANTS package where it is usually referred to as EXP1 (but not for all compilers!).

2. REPORT

You should hand in a report comprising the following sections:

1. Requirements
2. Design - including top down analysis, Nassi-Shneiderman and flow chart(s)
3. Implementation
4. Test cases and results as appropriate.

Marks distributed evenly between: design, implementation and testing. Refer to guidance notes on the presentation of work if necessary.

Created and maintained by Frans Coenen. Last updated 11 October 1999