# Probability and statistics symbols

## Probability and statistics symbols table

Symbol Symbol Name Meaning / definition Example
P(A) probability function probability of event A P(A) = 0.5
P(AB) probability of events intersection probability that of events A and B P(AB) = 0.5
P(A B) probability of events union probability that of events A or B P(AB) = 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
s2 sample variance population samples variance estimator s2 = 4
s sample standard deviation population samples standard deviation estimator s = 2
zx standard score

zx = (xx) / 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) = λeλx , x≥0
gamma(c, λ) gamma distribution

f (x) = λ c xc-1eλx / Γ(c), x≥0

χ 2(k) chi-square distribution

f (x) = xk/2-1ex/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) = λkeλ / 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