Probability theory and statistics have some commonly used conventions, in addition to standard mathematical notation and mathematical symbols.

- Random variables are usually written in upper case roman letters:
*X*,*Y*, etc. - Particular realizations of a random variable are written in corresponding lower case letters. For example,
*x*_{1},*x*_{2}, …,*x*_{n}could be a sample corresponding to the random variable*X*. A cumulative probability is formally written to differentiate the random variable from its realization. - The probability is sometimes written to distinguish it from other functions and measure
*P*so as to avoid having to define "*P*is a probability" and is short for , where is the event space and is a random variable. notation is used alternatively. - or indicates the probability that events
*A*and*B*both occur. The joint probability distribution of random variables*X*and*Y*is denoted as , while joint probability mass function or probability density function as and joint cumulative distribution function as . - or indicates the probability of either event
*A*or event*B*occurring ("or" in this case means one or the other or both). - σ-algebras are usually written with uppercase calligraphic (e.g. for the set of sets on which we define the probability
*P*) - Probability density functions (pdfs) and probability mass functions are denoted by lowercase letters, e.g. , or .
- Cumulative distribution functions (cdfs) are denoted by uppercase letters, e.g. , or .
- Survival functions or complementary cumulative distribution functions are often denoted by placing an overbar over the symbol for the cumulative:, or denoted as ,
- In particular, the pdf of the standard normal distribution is denoted by φ(
*z*), and its cdf by Φ(*z*). - Some common operators:

- E[
*X*] : expected value of*X* - var[
*X*] : variance of*X* - cov[
*X*,*Y*] : covariance of*X*and*Y*

- E[

- X is independent of Y is often written or , and X is independent of Y given W is often written

- or

- , the
*conditional probability*, is the probability of*given*, i.e.,*after*is observed.

- Greek letters (e.g. θ, β) are commonly used to denote unknown parameters (population parameters).
- A tilde (~) denotes "has the probability distribution of".
- Placing a hat, or caret, over a true parameter denotes an estimator of it, e.g., is an estimator for .
- The arithmetic mean of a series of values
*x*_{1},*x*_{2}, ...,*x*_{n}is often denoted by placing an "overbar" over the symbol, e.g. , pronounced "*x*bar". - Some commonly used symbols for sample statistics are given below:
- the sample mean ,
- the sample variance
*s*^{2}, - the sample standard deviation
*s*, - the sample correlation coefficient
*r*, - the sample cumulants
*k*._{r}

- Some commonly used symbols for population parameters are given below:
- the population mean
*μ*, - the population variance
*σ*^{2}, - the population standard deviation
*σ*, - the population correlation
*ρ*, - the population cumulants
*κ*,_{r}

- the population mean
- is used for the order statistic, where is the sample minimum and is the sample maximum from a total sample size
*n*.

The α-level upper critical value of a probability distribution is the value exceeded with probability α, that is, the value *x*_{α} such that *F*(*x*_{α}) = 1 − α where *F* is the cumulative distribution function. There are standard notations for the upper critical values of some commonly used distributions in statistics:

*z*_{α}or*z*(α) for the Standard normal distribution*t*_{α,ν}or*t*(α,ν) for the*t*-distribution with ν degrees of freedom- or for the chi-squared distribution with ν degrees of freedom
- or F(α,ν
_{1},ν_{2}) for the F-distribution with ν_{1}and ν_{2}degrees of freedom

- Matrices are usually denoted by boldface capital letters, e.g.
**A**. - Column vectors are usually denoted by boldface lowercase letters, e.g.
**x**. - The transpose operator is denoted by either a superscript T (e.g.
**A**^{T}) or a prime symbol (e.g.**A**′). - A row vector is written as the transpose of a column vector, e.g.
**x**^{T}or**x**′.

Common abbreviations include:

**a.e.**almost everywhere**a.s.**almost surely**cdf**cumulative distribution function**cmf**cumulative mass function**df**degrees of freedom (also )**i.i.d.**independent and identically distributed**pdf**probability density function**pmf**probability mass function**r.v.**random variable**w.p.**with probability;**wp1**with probability 1

- Glossary of probability and statistics
- Combinations and permutations
- Typographical conventions in mathematical formulae
- History of mathematical notation

- Halperin, Max; Hartley, H. O.; Hoel, P. G. (1965), "Recommended Standards for Statistical Symbols and Notation. COPSS Committee on Symbols and Notation",
*The American Statistician*,**19**(3): 12–14, doi:10.2307/2681417, JSTOR 2681417

- Earliest Uses of Symbols in Probability and Statistics, maintained by Jeff Miller.

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