### 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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