Discrete Probability Distribution
On a countable sample space with , knowing for all determines everything: the values form a discrete probability distribution, and for every .
Definition 2.18 (Discrete Probability Distribution)
Let be a probability space, where is countable with
If we know for all , then ,
In this case, we say that a discrete probability distribution.
We write for all .
Properties
Proposition 2.19 (Properties of Discrete Probability Distributions)
Let be a discrete probability distribution on a countable set . Then
-
for all .
-
.
Related
Stated in
- Definition 2.18 (Discrete Probability Distribution)§2.5 Discrete Probability Distributions
- Proposition 2.19 (Properties of Discrete Probability Distributions)§2.5 Discrete Probability Distributions