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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} \
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''.)
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