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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]