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(AB) probability of events intersection probability that of events A and B P(AB) = 0.5
P(AB) 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 symbol median middle value of random variable x example
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 example
∑∑ double summation double summation example
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    

Combinatorics Symbols

Symbol Symbol Name Meaning / definition Example
n! factorial n! = 1⋅2⋅3⋅...⋅n 5! = 1⋅2⋅3⋅4⋅5 = 120
nPk permutation _{n}P_{k}=frac{n!}{(n-k)!} 5P3 = 5! / (5-3)! = 60



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


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