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Statistical Symbols

Probability and statistics symbols table and definitions.

Probability and statistics symbols table

SymbolSymbol NameMeaning / definitionExample
P(A)probability functionprobability of event AP(A) = 0.5
P(AB)probability of events intersectionprobability that of events A and BP(AB) = 0.5
P(AB)probability of events unionprobability that of events A or BP(AB) = 0.5
P(A | B)conditional probability functionprobability of event A given event B occuredP(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) 
μpopulation meanmean of population valuesμ = 10
E(X)expectation valueexpected value of random variable XE(X) = 10
E(X | Y)conditional expectationexpected value of random variable X given YE(X | Y=2) = 5
var(X)variancevariance of random variable Xvar(X) = 4
σ2variancevariance of population valuesσ2 = 4
std(X)standard deviationstandard deviation of random variable Xstd(X) = 2
σXstandard deviationstandard deviation value of random variable XσX = 2
median symbolmedianmiddle value of random variable xexample
cov(X,Y)covariancecovariance of random variables X and Ycov(X,Y) = 4
corr(X,Y)correlationcorrelation of random variables X and Ycorr(X,Y) = 0.6
ρX,Ycorrelationcorrelation of random variables X and YρX,Y= 0.6
summationsummation - sum of all values in range of seriesexample
∑∑double summationdouble summationexample
Momodevalue that occurs most frequently in population 
MRmid-rangeMR = (xmax + xmin) / 2 
Mdsample medianhalf the population is below this value 
Q1lower / first quartile25% of population are below this value 
Q2median / second quartile50% of population are below this value = median of samples 
Q3upper / third quartile75% of population are below this value 
xsample meanaverage / arithmetic mean x = (2+5+9) / 3 = 5.333
s 2sample variancepopulation samples variance estimators 2 = 4
ssample standard deviation population samples standard deviation estimators = 2
zxstandard scorezx = (x-x) / sx 
X ~distribution of Xdistribution of random variable XX ~ N(0,3)
N(μ,σ2)normal distributiongaussian distributionX ~ N(0,3)
U(a,b)uniform distributionequal probability in range a,b  X ~ U(0,3)
exp(λ)exponential distributionf (x) = λe-λx ,x≥0 
gamma(c, λ)gamma distributionf (x) = λ c xc-1e-λx/ Γ(c), x≥0 
χ 2(k)chi-square distributionf (x) = xk/2-1e-x/2/ ( 2k/2 Γ(k/2) ) 
F (k1, k2)F distribution  
Bin(n,p)binomial distributionf (k) = nCkpk(1-p)n-k 
Poisson(λ)Poisson distributionf (k) = λke-λ/ k! 
Geom(p)geometric distributionf (k) =  p(1-p) k 
HG(N,K,n)hyper-geometric distribution  
Bern(p)Bernoulli distribution  

Combinatorics Symbols

SymbolSymbol NameMeaning / definitionExample
n!factorialn! = 1⋅2⋅3⋅...⋅n5! = 1⋅2⋅3⋅4⋅5 = 120
nPkpermutation_{n}P_{k}=\frac{n!}{(n-k)!}5P3 = 5! / (5-3)! = 60
nCk

 

combination

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