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Definition: Probability Mass Function

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]

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Bibliography (further reading)

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