Symbols:P

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pico-

$\mathrm p$

The Système Internationale d'Unités symbol for the metric scaling prefix pico, denoting $10^{\, -12 }$, is $\mathrm { p }$.


Its $\LaTeX$ code is \mathrm {p} .


peta-

$\mathrm P$

The Système Internationale d'Unités symbol for the metric scaling prefix peta, denoting $10^{\, 15 }$, is $\mathrm { P }$.


Its $\LaTeX$ code is \mathrm {P} .


Prime Number

$p$

Used to denote a general prime number.


The $\LaTeX$ code for \(p\) is p .


Probability

$p$

Used to denote a general probability.

As such, $p$ is a real number such that:

$0 \le p \le 1$


The $\LaTeX$ code for \(p\) is p .


Power Set

$\powerset S$ is the power set of the set $S$.

It is defined as:

$\powerset S = \set {T: T \subseteq S}$


$\map {\mathfrak P} S$ is an alternative notation, but the fraktur font, of which $\mathfrak P$ is an example, is falling out of use, probably as a result of its difficulty in being both read and written.


The $\LaTeX$ code for \(\powerset S\) is \powerset S .

The $\LaTeX$ code for \(\map {\mathfrak P} S\) is \map {\mathfrak P} S .


Poisson Distribution

$X \sim \Poisson \lambda$

or

$X \sim \map {\operatorname {Pois} } \lambda$


$X$ has the Poisson distribution with parameter $\lambda$.


The $\LaTeX$ code for \(X \sim \Poisson \lambda\) is X \sim \Poisson \lambda .

The $\LaTeX$ code for \(X \sim \map {\operatorname {Pois} } \lambda\) is X \sim \map {\operatorname {Pois} } \lambda .


Probability Measure

$\Pr$


Let $\mathcal E$ be an experiment.

Let $\Omega$ be the sample space on $\mathcal E$, and let $\Sigma$ be the event space of $\mathcal E$.


A probability measure on $\mathcal E$ is a mapping $\Pr: \Sigma \to \R$ which fulfils the Kolmogorov axioms.


The $\LaTeX$ code for \(\Pr\) is \Pr .


Probability Mass Function

$\map {p_X} x$


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:

$\forall x \in \R: \map {p_X} x = \begin{cases} \map \Pr {\set {\omega \in \Omega: \map X \omega = x} } & : x \in \Omega_X \\ 0 & : x \notin \Omega_X \end{cases}$

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 $x$.


The $\LaTeX$ code for \(\map {p_X} x\) is \map {p_X} x .