Let \(X\) be a random variable of a given random experiment. Assume, we have a random experiment, for which the probability of the event

“\(X\) has a realization equal a given real number \(x\)”,

i.e. the probability \(p(X = x)\) exists for all real numbers \(x\in\mathbb R\).

Then we call the function

\[f:=\cases{\mathbb R\mapsto[0,1]\\x\mapsto p(X=x)}\quad\quad\text{for all }x\in\mathbb R\]

the **probability mass function** (or (**pmf**) of the random variable \(X\).

| | | | | created: 2016-03-25 16:22:59 | modified: 2016-03-25 16:24:14 | by: *bookofproofs* | references: [1796]

[1796] **Hedderich, J.;Sachs, L.**: “Angewandte Statistik”, Springer Gabler, 2012, Vol .14