Category:Examples of Probability Mass Functions
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This category contains examples of Probability Mass Function.
Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space.
Let $X: \Omega \to \R$ be a discrete random variable on $\struct {\Omega, \Sigma, \Pr}$.
Then the probability mass function of $X$ is the (real-valued) function $p_X: \R \to \closedint 0 1$ defined as:
$\quad \forall x \in \R: \map {p_X} x = \begin {cases} \map \Pr {\set {\omega \in \Omega: \map X \omega = x} } & : x \in \Omega_X \\ 0 & : x \notin \Omega_X \end {cases}$
where $\Omega_X$ is defined as $\Img X$, the image of $X$.
That is, $\map {p_X} x$ is the probability that the discrete random variable $X$ takes the value $x$.
Pages in category "Examples of Probability Mass Functions"
The following 4 pages are in this category, out of 4 total.