Probability and statistics symbols table and definitions.
| Symbol | Symbol Name | Meaning / definition | Example |
|---|---|---|---|
| P(A) | probability function | probability of event A | P(A) = 0.5 |
| P(A ∩ B) | probability of events intersection | probability that of events A and B | P(A∩B) = 0.5 |
| P(A ∪ B) | probability of events union | probability that of events A or B | P(A ∪ B) = 0.5 |
| P(A | B) | conditional probability function | probability of event A given event B occured | P(A | B) = 0.3 |
| f (x) | probability density function (pdf) | P(a ≤ x ≤ b) = ∫ f (x) dx | |
| F(x) | cumulative distribution function (cdf) | F(x) = P(X≤ x) | |
| μ | population mean | mean of population values | μ = 10 |
| x | average or arithmetic mean | sum of values divided by the count of values | x = (5+10+2) / 3 |
| E(X) | expectation value | expected value of random variable X | E(X) = 10 |
| E(X | Y) | conditional expectation | expected value of random variable X given Y | E(X | Y=2) = 5 |
| var(X) | variance | variance of random variable X | var(X) = 4 |
| σ2 | variance | variance of population values | σ2 = 4 |
| std(X) | standard deviation | standard deviation of random variable X | std(X) = 2 |
| σX | standard deviation | standard deviation value of random variable X | σX = 2 |
 |
median | middle value of random variable x |  |
| cov(X,Y) | covariance | covariance of random variables X and Y | cov(X,Y) = 4 |
| corr(X,Y) | correlation | correlation of random variables X and Y | corr(X,Y) = 0.6 |
| ρX,Y | correlation | correlation of random variables X and Y | ρX,Y = 0.6 |
| ∑ | summation | summation - sum of all values in range of series |  |
| ∑∑ | double summation | double summation |  |
| Mo | mode | value that occurs most frequently in population | |
| MR | mid-range | MR = (xmax + xmin) / 2 | |
| Md | sample median | half the population is below this value | |
| Q1 | lower / first quartile | 25% of population are below this value | |
| Q2 | median / second quartile | 50% of population are below this value = median of samples | |
| Q3 | upper / third quartile | 75% of population are below this value | |
| x | sample mean | average / arithmetic mean | x = (2+5+9) / 3 = 5.333 |
| s 2 | sample variance | population samples variance estimator | s 2 = 4 |
| s | sample standard deviation | population samples standard deviation estimator | s = 2 |
| zx | standard score | zx = (x-x) / sx | |
| X ~ | distribution of X | distribution of random variable X | X ~ N(0,3) |
| N(μ,σ2) | normal distribution | gaussian distribution | X ~ N(0,3) |
| U(a,b) | uniform distribution | equal probability in range a,b | X ~ U(0,3) |
| exp(λ) | exponential distribution | f (x) = λe-λx , x≥0 | |
| gamma(c, λ) | gamma distribution | f (x) = λ c xc-1e-λx / Γ(c), x≥0 | |
| χ 2(k) | chi-square distribution | f (x) = xk/2-1e-x/2 / ( 2k/2 Γ(k/2) ) | |
| F (k1, k2) | F distribution | ||
| Bin(n,p) | binomial distribution | f (k) = nCk pk(1-p)n-k | |
| Poisson(λ) | Poisson distribution | f (k) = λke-λ / k! | |
| Geom(p) | geometric distribution | f (k) = p(1-p) k | |
| HG(N,K,n) | hyper-geometric distribution | ||
| Bern(p) | Bernoulli distribution |
| Symbol | Symbol Name | Meaning / definition | Example |
|---|---|---|---|
| n! | factorial | n! = 1⋅2⋅3⋅...⋅n | 5! = 1⋅2⋅3⋅4⋅5 = 120 |
| nPk | permutation |  |
5P3 = 5! / (5-3)! = 60 |
| nCk
|
combination |  |
5C3 = 5!/[3!(5-3)!]=10 |
