Probabilistic Variables

Definition

A model for describing the outcome of a random experiment or observation, underlying the laws of probability. A discrete and finite probabilistic variable X is characterized by

• 1. A set of possible outcomes $\mathcal{X}$ = {x ₁, … x _k } of a random experiment

• 2. A probability p(x) for each outcome x ∼ $\mathcal{X}$, which is a nonnegative real number with the following properties (see also Probability Distributions):

$$ p(x) \geq 0 \quad {\text{for}}\,{\text{all}}\,{\text{outcomes}}\,x \in \mathcal{X} $$

(1)

$$ \sum\limits_{{x \in \mathcal X}} {p(x) = 1.} $$

(2)

The characterization assumes that the outcomes in $\mathcal{X}$ are both complete (i.e., every possible outcome is covered by some x _i ) and mutually exclusive (i.e., there is no possibility for X to have two different outcomes x _i and x _j simultaneously).

Joint probabilistic variablesare probabilistic variables whose outcomes are linked, often resulting from experiments or observations with...