Notation

Every article uses the same symbols for the same ideas. Each article still defines its notation when it first appears, so you should not need this page to read an article; it is here as a reference.

Probability

Symbol	Meaning
$\Omega$	the sample space: the set of all possible outcomes
$A, B$	events (subsets of $\Omega$ )
$P(A)$	the probability of event $A$
$A^c$	the complement of $A$ : “ $A$ does not happen”
$A \cap B$ , $A \cup B$	“both $A$ and $B$ ”, “ $A$ or $B$ or both”
$P(A \mid B)$	the conditional probability of $A$ given $B$

Random variables and distributions

Symbol	Meaning
$X, Y$	random variables (capital letters)
$x, y$	particular values they can take (lower-case letters)
$p(x) = P(X = x)$	probability mass function (PMF) of a discrete variable
$f(x)$	probability density function (PDF) of a continuous variable
$F(x) = P(X \le x)$	cumulative distribution function (CDF)
$X \sim \mathcal{N}(\mu, \sigma^2)$	“ $X$ has a normal distribution with mean $\mu$ and variance $\sigma^2$ ”
$\E[X]$	expected value (mean) of $X$
$\Var(X)$	variance of $X$
$\Cov(X, Y)$ , $\Corr(X, Y)$	covariance and correlation of $X$ and $Y$
$Z$ , $\varphi$ , $\Phi$	a standard normal variable, its density, and its CDF
$H_0$ , $H_1$ , $\alpha$	null hypothesis, alternative hypothesis, significance level

A probability mass $p(x)$ is a probability. A density $f(x)$ is not: probabilities for continuous variables are areas under $f$ .

Populations, samples, and estimates

Symbol	Meaning
$\mu$ , $\sigma^2$ , $\sigma$	population mean, variance, standard deviation
$n$	sample size
$x_1, \dots, x_n$	observed data values
$\bar{x} = \frac{1}{n}\sum_{i=1}^n x_i$	sample mean
$s^2 = \frac{1}{n-1}\sum_{i=1}^n (x_i - \bar{x})^2$	sample variance (note the $n - 1$ )
$s$	sample standard deviation
$\theta$	a generic parameter
$\hat{\theta}$	an estimate or estimator of $\theta$ (the “hat” marks an estimate)
$\bar{X}$	the sample mean viewed as a random variable
$\bar{X}_n$	the sample mean of the first $n$ observations, when the dependence on $n$ matters
$s_{xy}$ , $r$	sample covariance and sample correlation of paired data
$\rho$	population correlation

Other conventions

$\log$ is the natural logarithm (base $e$ ).
$\exp(u)$ means $e^u$ .
$\sum_{i=1}^n$ is a sum over $i = 1, 2, \dots, n$ .
$\binom{n}{k} = \frac{n!}{k!\,(n-k)!}$ is the number of ways to choose $k$ items from $n$ .
The letter $p$ is used both for a success probability (as in the binomial distribution) and for a p-value. Where both appear together, the success probability is written $\theta$ instead.
Probabilities are written as decimals ( $0.25$ ) or percentages (25%), whichever reads more naturally.