Content deleted Content added
Line 3:
==Mathematical description==
Suppose that ''X'' is a [[discrete random variable]], taking values on some [[countable]] [[sample space]] ''S'' ⊆ '''R'''. Then the probability mass function ''f''<sub>''X''</sub>(''x'') for ''X'' is given by
:<math>f_X(x) = \begin{cases} \Pr(X = x), &x\in S,\\0, &x\in \mathbb{R}\backslash S.\end{cases}</math>
Note that this explicitly defines ''f''<sub>''X''</sub>(''x'') for all [[real number]]s, including all values in '''R''' that ''X'' could never take; indeed, it assigns such values a probability of zero. (Alternatively, think of Pr(''X'' = ''x'') as 0 when ''x'' ∈ '''R'''\''S''.)
| |||