Probability mass function: Difference between revisions

Revision as of 23:50, 4 December 2003

Revision as of 04:31, 5 December 2003

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==Mathematical description==

Suppose that ''X'' is a discrete random variable, that is, that it takestaking values on some [[countable]] [[sample space]] ''S''. We may assume that ''S'' ⊂ '''R''' (this will suffice, but more accurately  ''XS''  is a function, &nbspsube;''X'': ''S''→'''R'''). Then the probability mass function  ''f''_''X''(''x'')  for ''X'' is given by

:<math>f_X(x) = \begin{cases}\mathrm{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''.)