For a finite or countable set 
and a given summable sequence of
non-negative numbers 
put
In probability theory it is customary to denote
and rewrite (
) as 
.
Formula () generalizes the uniform assignment (),
which corresponds to the choice of equal weights
.
At the same time it is more
flexible
and applies also to infinite sample spaces.
Table list the most frequently encountered discrete probability
assignments.
| Name |  | Probabilities  |
| Binomial |  |  |
| Poisson |  |  |
| Geometric |  |  |
| Equally likely outcomes |  |  |
The reasons behind the particular choices of the expressions for in Table
involve modeling.
