## 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) = 0.5P(A∩B)probability of events intersection probability that of events A and B P(A∩B) = 0.5P(A∪B)probability of events union probability that of events A or B P(A∪B) = 0.5P(A|B)conditional probability function probability of event A given event B occured P(A | B) = 0.3f(x)probability density function (pdf) P(a≤x≤b) =∫ f(x)dxF(x)cumulative distribution function (cdf) F(x) =P(X≤x)μpopulation mean mean of population values μ= 10E(X)expectation value expected value of random variable X E(X) = 10E(X | Y)conditional expectation expected value of random variable X given Y E(X | Y=2) = 5var(X)variance variance of random variable X var(X) = 4σ ^{2}variance variance of population values σ = 4^{2 }std(X)standard deviation standard deviation of random variable X std(X) = 2σ _{X}standard deviation standard deviation value of random variable X σ =_{X}_{ }2median middle value of random variable x cov(X,Y)covariance covariance of random variables X and Y cov(X,Y) = 4corr(X,Y)correlation correlation of random variables X and Y corr(X,Y) = 0.6ρ_{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 Momode value that occurs most frequently in population MRmid-range

MR= (x+_{max}x)/2_{min}Mdsample median half the population is below this value Q _{1}lower / first quartile 25% of population are below this value Q _{2}median / second quartile 50% of population are below this value = median of samples Q _{3}upper / third quartile 75% of population are below this value xsample mean average / arithmetic mean x= (2+5+9) / 3 = 5.333s_{ }^{2}sample variance population samples variance estimator s^{ }^{ 2}= 4ssample standard deviation population samples standard deviation estimator s= 2z_{x}standard score

z= (_{x}x-x) /s_{x}X~distribution of X distribution of random variable X X~N(0,3)N(μ,σ^{2})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≥0gamma(c, λ)gamma distribution

f(x)= λ c x^{c-1}e^{-λx}/ Γ(c),x≥0χ ^{ 2}(k)chi-square distribution

f(x)= x^{k}^{/2-1}e^{-x/2}/ ( 2^{k/2 }Γ(k/2) )F(k_{1}, k_{2})F distribution Bin(n,p)binomial distribution

f(k)=(1_{n}C_{k}p^{k}-p)^{n-k}Poisson(λ)Poisson distribution

f(k)= λ^{k}e^{-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·...·n5! = 1·2·3·4·5 = 120 _{n}P_{k}permutation _{5}P_{3}=5! / (5-3)! = 60_{n}C_{k}

combination _{5}C_{3}=5!/[3!(5-3)!]=10

## See also