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title: "Probability mass function - pmf"
canonical: "https://modelassist.epixanalytics.com/space/EA/26574887/Probability%20mass%20function%20-%20pmf"
format: markdown
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If a random variable *X* is discrete, i.e. it may take any of a specific set of *n* values *x**i*, *i* = 1 to *n*, then:


            *P*(*X*=*x*<sub>*i*</sub>) = *p*(*x*<sub>*i*</sub>)


*p(x)* is called the *probability mass function*

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| --- | --- |
| Note that | ![image](media://c7cd4ad6-5736-4ef2-957e-4d5f31afcb4b)<br>> Macro (mathinline) |

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| --- | --- |
| and       *F*(*x*<sub>*k*</sub>) = | ![image](media://099f9d51-c91a-45b4-bebe-556dc0dcbc72)<br>> Macro (mathinline) |



*For example, if a coin is tossed 3 times, the number of observed heads is discrete. The possible values of **x**i** are:*

![image](media://f075eaf1-36ac-4279-b08a-8e3a160db88c)


In ModelAssist we use the notation f(x) and p(x) interchangeably for a probability mass function.




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