### Probability Distribution

**Definition: **
A *probability distribution*
may be defined as a
non-negative real function of all possible outcomes of some random
event. The sum of the probabilities of all possible outcomes is
defined as 1, and probabilities can never be negative.

**Example: **
A *coin toss* has two outcomes, ``heads'' (H) or ``tails'' (T),
which are equally likely if the coin is ``fair''. In this case, the
probability distribution is

(C.1) |

where denotes the

*probability*of outcome . That is, the total ``probability mass'' is divided equally between the two possible outcomes heads or tails. This is an example of a

*discrete*probability distribution because all probability is assigned to two discrete points, as opposed to some continuum of possibilities.

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