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Next: 2.1.4 Probability densities Up: 2.1 Probabilities and Random Previous: 2.1.2 Random Variables

2.1.3 Probability Distributions

The randomness of a discrete random variable (r.v.) $ X$ is characterized by its probability distribution.

Definition 6   The probability distribution of a discrete r.v. $ X$ is the function:

$\displaystyle P_{X}(x) = P(X(w) = x) = P(\{w: X(w)=x\}) $

where $ P$ is the (underline) probability on $ \Omega$.

Remark:

$\displaystyle \sum_x P_X(x) = 1 $



Eran Borenstein
2007-05-04