Difference between revisions of "Probability mass function"
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| − | In [[probability theory]], a '''probability mass function''' | + | In [[probability theory]], a '''probability mass function''' (''p(x)'') is a real-valued function of a discrete variable (''x''), such that the value ''p(x<sub>k</sub>)'' is the probability of the variable ''x'' having the value x<sub>k</sub>. |
In order to qualify, such a function must meet the following criteria: | In order to qualify, such a function must meet the following criteria: | ||
| − | <math>p(x_{k}) \geq 0 | + | *<math>p(x_{k}) \geq 0; \forall x </math> |
| + | *<math>\sum_{k} p(x_{k}) = 1 </math> | ||
| − | + | The collection of pairs ( x<sub>k</sub> , p(x<sub>k</sub>) ) is the [[discrete]] [[probability distribution]] of ''x''. | |
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| − | The collection of pairs ( x<sub>k</sub> , p(x<sub>k</sub>) ) is the | ||
[[Category:mathematics]] | [[Category:mathematics]] | ||
Revision as of 20:09, March 30, 2008
In probability theory, a probability mass function (p(x)) is a real-valued function of a discrete variable (x), such that the value p(xk) is the probability of the variable x having the value xk.
In order to qualify, such a function must meet the following criteria:
- <math>p(x_{k}) \geq 0; \forall x </math>
- <math>\sum_{k} p(x_{k}) = 1 </math>
The collection of pairs ( xk , p(xk) ) is the discrete probability distribution of x.