Probability mass function: Difference between revisions

Revision as of 07:51, 15 August 2005

Revision as of 07:52, 15 August 2005

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SuppposeSuppose that ''X'' is a discrete random variable, taking values on some [[countable]] [[sample space]]  ''S'' ⊆ '''R'''. Then the probability mass function  ''f''_''X''(''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 &nbsp;''f''_''X''(''x'')&nbsp; 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 &nbsp;Pr(''X'' = ''x'')&nbsp; as 0 when &nbsp;''x'' &isin; '''R'''\''S''.)