Probability and statistics symbols

Statistical Symbols

Probability and statistics symbols table and definitions.

Probability and statistics symbols table

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
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 x^c-1e^-λx / Γ(c), x≥0

χ ²(k)
chi-square distribution

f (x) = x^k/2-1e^-x/2 / ( 2^k/2 Γ(k/2) )

F (k₁, k₂)
F distribution


Bin(n,p)
binomial distribution

f (k) = _nC_k p^k(1-p)^n-k

Poisson(λ)
Poisson distribution

f (k) = λ^ke^-λ / k!

Geom(p)
geometric distribution

f (k) =  p (1-p) ^k

HG(N,K,n)
hyper-geometric distribution


Bern(p)
Bernoulli distribution

Combinatorics Symbols

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