$\DeclareMathOperator{\p}{P}$ $\DeclareMathOperator{\P}{P}$ $\DeclareMathOperator{\c}{^C}$ $\DeclareMathOperator{\or}{ or}$ $\DeclareMathOperator{\and}{ and}$ $\DeclareMathOperator{\var}{Var}$ $\DeclareMathOperator{\Var}{Var}$ $\DeclareMathOperator{\Std}{Std}$ $\DeclareMathOperator{\E}{E}$ $\DeclareMathOperator{\std}{Std}$ $\DeclareMathOperator{\Ber}{Bern}$ $\DeclareMathOperator{\Bin}{Bin}$ $\DeclareMathOperator{\Poi}{Poi}$ $\DeclareMathOperator{\Uni}{Uni}$ $\DeclareMathOperator{\Geo}{Geo}$ $\DeclareMathOperator{\NegBin}{NegBin}$ $\DeclareMathOperator{\Beta}{Beta}$ $\DeclareMathOperator{\Exp}{Exp}$ $\DeclareMathOperator{\N}{N}$ $\DeclareMathOperator{\R}{\mathbb{R}}$ $\DeclareMathOperator*{\argmax}{arg\,max}$ $\newcommand{\d}{\, d}$

Notation Reference


Core Probability

Notation Meaning
$E \text{ or } F$ Capital letters can denote events
$A \text{ or } B$ Sometimes they denote sets
$|E| $ Size of an event or set
$E^C$ Complement of an event or set
$EF$ And of events (aka intersection)
$ E \and F$ And of events (aka intersection)
$ E \cap F$ And of events (aka intersection)
$ E \or F$ Or of events (aka union)
$ E \cup F$ Or of events (aka union)
$\p(E)$ The probability of an event $E$
$\p(E|F)$ The conditional probability of an event $E$ given $F$
$\p(E,F)$ The probability of event $E$ and $F$
$\p(E|F,G)$ The conditional probability of an event $E$ given both $F$ and $G$
$n!$ $n$ factorial
${n \choose k}$ Binomial coefficient
${n \choose {r_1,r_2,r_3} }$ Multinomial coefficient

Random Variables

Notation Meaning
$x \text{ or } y \text{ or } i$ Lower case letters denote regular variables
$X \text{ or } Y$ Capital letters are used to denote random variables
$K$ Capital $K$ is reserved for constants
$\E[X]$ Expectation of $X$
$\Var(X)$ Variance of $X$
$\p(X=x)$ Probability mass function (PMF) of $X$, evaluated at $x$
$\p(x)$ Probability mass function (PMF) of $X$, evaluated at $x$
$f(X=x)$ Probability density function (PDF) of $X$, evaluated at $x$
$f(x)$ Probability density function (PDF) of $X$, evaluated at $x$
$f(X=x,Y=y)$ Joint probability density
$f(X=x|Y=y)$ Conditional probability density
$F_X(x)$ or $F(x)$ Cumulative distribution function (CDF) of $X$
IID Independent and Identically Distributed

Parametric Distributions

Notation Meaning
$X \sim \Ber(p)$ $X$ is a Bernoulli random variable
$X \sim \Bin(n,p)$ $X$ is a Binomial random variable
$X \sim \Poi(p)$ $X$ is a Poisson random variable
$X \sim \Geo(p)$ $X$ is a Geometric random variable
$X \sim \NegBin(r, p)$ $X$ is a Negative Binomial random variable
$X \sim \Uni(a,b)$ $X$ is a Uniform random variable
$X \sim \Exp(\lambda)$ $X$ is a Exponential random variable
$X \sim \Beta(a,b)$ $X$ is a Beta random variable