Discrete Probability Space

probability-theory

Definition

Discrete Probability Space

A discrete probability space is a probability space $(\Omega ,\mathfrak{S},P)$ where the sample space is countable.

$$\Omega =\{{\omega }_1,{\omega }_2,\dots \}$$

Probability Mass Function

The probability mass function is uniquely defined by the probability of elementary events:

$$p_i=P(\{{\omega }_i\})$$

with:

$$0\le p_i\le 1,\sum _i{p}_i=1$$