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

Probability theory

• Random variables are usually written in upper case is written, then it represents the probability that a particular realisation of a random variable (e.g., height, number of cars, or bicycle colour), X is a value. Clearly they are related, but they do not have identical meanings.

• Particular realisations of a random variable are written in corresponding lower case could be a sample to distinguish the random variable from its realization.

• to distinguish it from other functions and measure P to avoid having to define "P notation is used alternatively.

• indicates the probability that events A and B both occur. The joint probability distribution of random variables X and Y.

• 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 for the set of sets on which we define the probability P)

• Probability density functions (pdfs) and probability mass functions.

• Cumulative distribution functions.

• Survival functions or complementary cumulative distribution functions are often denoted by placing an overbar,

• In particular, the pdf of the standard normal distribution.

• Some common operators:

• : expected value of X

• : variance of X

• : covariance of X and Y

• , and X is independent of Y given W is often written

• or

• , the conditional probability given

Statistics

• Greek letters (e.g. , ) are commonly used to denote unknown parameters (population parameters).

Some commonly used symbols for population or distribution parameters are given below:

• ,

• ,

• the population standard deviation ,

• the population correlation ,

• the population cumulants ,

• A tilde (~) denotes "has the probability distribution of".

• Placing a hat, or caret (also known as a circumflex), over a true parameter denotes an estimator.

• The arithmetic mean is often denoted by placing an "overbar bar".

Some commonly used symbols for sample statistics are given below:

• the sample mean,

• the sample variance,

• the sample standard deviation ,

• the sample correlation coefficient ,

• .

• order statistic.

Critical values

The α-level upper critical value of a probability distribution is the cumulative distribution function. There are standard notations for the upper critical values of some commonly used distributions in statistics:

• for the standard normal distribution

• for the t-distribution degrees of freedom

• for the chi-squared distribution degrees of freedom

• for the F-distribution degrees of freedom

Linear algebra

• Matrices.

• Column vectors are usually denoted by boldface lowercase letters, e.g. .

• The transpose operator is denoted by either a superscript T (e.g. ) or a prime symbol (e.g. ).

• A row vector is written as the transpose of a column vector, e.g. or .

Abbreviations

Common abbreviations include:

• a.e. almost everywhere

• a.s. almost surely

• cdf cumulative distribution function

• cmf cumulative mass function

• df degrees of freedom)

• 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

• i.o.

• ult.

See also

• Glossary of probability and statistics

• Combinations and permutations

• History of mathematical notation

References

External links

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