Statistical symbols & probability symbols (μ,σ,...)

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

σ_X standard deviation standard deviation value of random variable X σ_X = 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

ρ_X,Y correlation correlation of random variables X and Y ρ_X,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 = (x_max+x_min)/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 s² = 4

s sample standard deviation population samples standard deviation estimator s = 2

z_x standard score
z_x = (x-x) / s_x

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

χ²(k) chi-square distribution
f (x) = x^k^/2-1e^-x/2 / ( 2^k/2Γ(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

_nP_k permutation $_{n}P_{k}=\frac{n!}{(n-k)!}$ ₅P₃ = 5! / (5-3)! = 60

_nC_k

combination $_{n}C_{k}=\binom{n}{k}=\frac{n!}{k!(n-k)!}$ ₅C₃ = 5!/[3!(5-3)!]=10

Set symbols ►

See also

Math symbols

Set symbols

Basic math symbols

Logic symbols

Greek alphabet symbols

Probability distribution

Probability & statistics

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
σ_X	standard deviation	standard deviation value of random variable X	σ_X = 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
ρ_X,Y	correlation	correlation of random variables X and Y	ρ_X,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 = (x_max+x_min)/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	s² = 4
s	sample standard deviation	population samples standard deviation estimator	s = 2
z_x	standard score	z_x = (x-x) / s_x
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
χ²(k)	chi-square distribution	f (x) = x^k^/2-1e^-x/2 / ( 2^k/2Γ(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

Statistical Symbols

Probability and statistics symbols table

Combinatorics Symbols

See also

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