Normalisation (probability)

In mathematical probability equations, which are used in nearly all branches of science, a normalization constant is often used to ensure that the sum of all probabilites totals one. The normalization contant is then simply one divided by the sum of all probabilitiies

$N={\frac {1}{\sum P_{i}}}$

Probability distributions can be divided into two main groups, discrete probability distributions and continuous probability distributions.

Discrete Probabilty Distributions

Discrete probability distributions are used througout gaming theory. Consider the simple example of rolling a pair of six-sided dice. Summing up the total roll of the dice yields the following possibilities:

Total (i)	Possible outcomes (Dice1,Dice2)	occurances (ni)
2	(1,1)	1
3	(1,2), (2,1)	2
4	(1,3), (3,1), (2,2)	3
5	(1,4), (4,1), (2,3), (3,2)	4
6	(1,5), (5,1), (2,4), (4,2), (3,3)	5
7	(1,6), (6,1), (2,5), (5,2), (3,4), (4,3)	6
8	(2,6), (6,2), (5,3), (3,5), (4,4)	5
9	(3,6), (6,3), (4,5), (5,4)	4
10	(4,6), (6,4), (5,5)	3
11	(5,6), (6,5)	2
12	(6,6)	1

So for this system, the normalization constant, N, is the number one