Symbols:P

General 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

$\mathcal P \left({S}\right)$ is the power set of the set $S$.

It is defined as: $\mathcal P \left({S}\right) = \left\{ {T: T \subseteq S}\right\}$.

$\mathfrak P \left({S}\right)$ 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 $\mathcal P \left({S}\right)$ is \mathcal P \left({S}\right).

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

Poisson Distribution

$X \sim \operatorname{Pois} \left({\lambda}\right)$

or

$X \sim \operatorname{Poisson} \left({\lambda}\right)$

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

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

The $\LaTeX$ code for $X \sim \operatorname{Poisson} \left({\lambda}\right)$ is X \sim \operatorname{Poisson} \left({\lambda}\right).

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

$p_X \left({x}\right)$

Let $\left({\Omega, \Sigma, \Pr}\right)$ be a probability space.

Let $X: \Pr \to \R$ be a discrete random variable on $\left({\Omega, \Sigma, \Pr}\right)$.

Then the (probability) mass function or p.m.f. of $X$ is the function $p_X: \R \to \left[{0 .. 1}\right]$ defined as:

$\forall x \in \R: p_X \left({x}\right) = \begin{cases} \Pr \left({\left\{{\omega \in \Omega: X \left({\omega}\right) = x}\right\}}\right) & : x \in \Omega_X \\ 0 & : x \notin \Omega_X \end{cases}$

where $\Omega_X$ is defined as $\operatorname{Im} \left({X}\right)$, the image of $X$.

That is, $p_X \left({x}\right)$ is the probability that the function $X$ takes the value $x$.

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