Probability Symbols, Names, and Explanations Every Statistician Should Know

probability symbolsMost people are familiar with basic arithmetic symbols, like the addition, subtraction, multiplication, and division signs. When it comes to higher level mathematics like statistics and probability, there are whole new sets of symbols used to represent its concepts and formulas.

In this guide, you’ll find an extensive list of probability symbols you can use for reference, plus the names of each symbol and the concept they represent. Check out this introductory statistics course for more on entry-level probability concepts.

Before you get into the probability symbols and their meanings, you’ll need to memorize the letters of the Greek alphabet, since many of them are used to represent specific variables or ideas in upper level math. Check out this course on New Testament Greek to learn its alphabet.

Probability Symbols and Explanations

Below you’ll find a list of probability symbols. For a more advanced explanation of what these symbols are used for in probability and statistics, check out this course on descriptive statistics and this course on inferential statistics.

  • P(A)

Name: Probability function.
Explanation: Used to represent the probability of event A.

  • P(A ∩ B)

Name: Probability of events intersection.
Explanation: Used to represent the probability of both event A and event B.

  • P(A  B)

Name: Probability of events union.
Explanation: Used to represent the probability of event A or event B.

  • P(A | B)

Name: Conditional probability function.
Explanation: Used to represent the probability of Event A.

  • (x)

Name: Probability density function.

Probability is both theoretical and practical in terms of its applications. To learn more about its basic concepts and functions, and how these symbols play a role in them, check out this probability for beginners foundational course.

  • μ

Name: Population mean.
Explanation: Used to represent the mean of population values.

  • E(X)

Name: Expectation value.
Explanation: Used to represent the expected value of variable X.

  • E(X | Y)

Name: Conditional expectation.
Explanation: Used to represent the expected value of variable X, given variable Y.

  • var(X)

Name: Variance.
Explanation: Used to represent the variance of variable X.

  • σ2

Name: Variance.
Explanation: Used to represent the variance of population values.

  • std(X)

Name: Standard deviation.
Explanation: Used to represent the standard deviation of variable X.

Standard deviation shows how much dispersion there is from the average in a set of data. This is connected to mean, median, and mode as well, which are also statistics concepts. To find out more, check out this guide on standard deviation.

  • cov(X,Y)

Name: Covariance.
Explanation: Used to represent the covariance of variables X and Y.

  • corr(X,Y)

Name: Correlation.
Explanation: Used to represent the correlation of variables X and Y.

  • ρX,Y

Name: Correlation.
Explanation: Same as above.

Name: Summation.
Explanation: Used to represent the sum of all values that are in range in a series.

  • ∑∑

Name: Double summation.
Explanation: Same as above, but doubled!

Summation is also present in calculus. Check out this calculus course on integers for a more in-depth explanation of the concept and related functions.

  • Q1

Name: First quartile.
Explanation: Used to represent the 25% of the population below this value.

  • Q2

Name: Second quartile.
Explanation: Used to represent the 50% of the population below this value.

  • Q3

Name: Third quartile.
Explanation: Used to represent the 75% of the population below this value.

  • n!

Name: Factorial.

  • nPk

Name: Permutation.

  • N(μ,σ2)

Name: Normal distribution.

  • U(a,b)

Name: Uniform distribution.

  • exp(λ)

Name: Exponential distribution.

  • gamma(c, λ)

Name: Gamma distribution.

  • χ 2(k)

Name: Chi-square distribution.

  • (k1, k2)

Name: F distribution.

  • Bin(n,p)

Name: Binomial distribution.

  • Poisson(λ)

Name: Poisson distribution.

  • Geom(p)

Name: Geometric distribution.

  • HG(N,K,n)

Name: Hyper-geometric distribution.

  • Bern(p)

Name: Bernoulli distribution.

Besides mathematical symbols and formulas, there are a number of theory symbols you should know as well. If this is all going over your head, you might want to consider checking out this introductory statistics course before moving on.

  •  B – Intersection
  •  B – Union
  •  B – Subset
  •  B – Strict subset
  •  B – Not subset
  •  B – Superset
  •  B – Proper superset
  •  B – Not superset
  • A = B – Equality
  • A \ B – Relative complement
  • A – B – Relative complement
  • A ∆ B – Symmetric difference
  •  B – Symmetric difference
  • aA – Element of
  • xA – Not element of
  • (a,b) – Ordered pair
  • A×B – Cartesian product
  • |A| – Cardinality
  • #A – Cardinality
  • Ø – Empty set
  • { } – Set; collections elements such as numbers
  • | – “Such that”

Consider checking out this course for an introductory look at probability, or this entry-level probability course on the applications of probability day to day.