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Probability and statistics symbols table and definitions.

Probability and statistics symbols tableSymbol Symbol Name Meaning / definition Example

probabilityfunction probability of event A P(A) = 0.5

probability ofeventsintersection

probability that ofevents A and B P(AB) = 0.5

probability ofevents unionprobability that ofevents A or B P(AB) = 0.5

conditionalprobabilityfunction

probability of event Agiven event B occured P(A | B) = 0.3

probabilitydensity function(pdf)

P(a x b) = f (x)dx

cumulativedistributionfunction (cdf)

F(x) = P(X x)

population mean mean of populationvalues = 10expectationvalue

expected value ofrandom variable X E(X) = 10

conditionalexpectation

expected value ofrandom variable Xgiven Y

E(X | Y=2) = 5

variance variance of randomvariable X var(X) = 4

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2 variance variance of populationvalues 2 = 4standarddeviation

standard deviation ofrandom variable X std(X) = 2

Xstandarddeviation

standard deviationvalue of randomvariable X

X = 2

median middle value ofrandom variable x

covariance covariance of randomvariables X and Y cov(X,Y) = 4

correlation correlation of randomvariables X and Y corr(X,Y) = 0.6

X,Y correlationcorrelation of randomvariables X and Y

X,Y = 0.6

summationsummation - sum of allvalues in range ofseries

doublesummation double summation

modevalue that occurs mostfrequently inpopulation

mid-range MR = (xmax+xmin)/2

sample median half the population isbelow this value

1lower / firstquartile

25% of population arebelow this value

2median / secondquartile

50% of population arebelow this value =median of samples

3upper / thirdquartile

75% of population arebelow this value

sample mean average / arithmeticmean x = (2+5+9) / 3 = 5.333

2 sample variance population samplesvariance estimator s

2 = 4

sample standarddeviation

population samplesstandard deviationestimator

s = 2

x standard score zx = (x-x) / sx

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distribution of X distribution of randomvariable X X ~ N(0,3)

N(,2) normaldistribution gaussian distribution X ~ N(0,3)

U(a,b) uniformdistributionequal probability inrange a,b X ~ U(0,3)

exp() exponentialdistribution f (x) = e-x , x0

gamma(c, ) gammadistributionf (x) = c xc-1e-x /(c), x0

2(k) chi-squaredistributionf (x) = xk/2-1e-x/2 / (2k/2 (k/2) )

F (k1, k

2) F distribution

Bin(n,p) binomialdistribution f (k) = nCk pk(1-p)n-k

Poisson() Poissondistribution f (k) = ke- / k!

Geom(p) geometricdistribution f (k) = p (1-p) k

HG(N,K,n) hyper-geometricdistribution

Bern(p) Bernoullidistribution

Combinatorics Symbols

Symbol SymbolName Meaning / definition Example

factorial n! = 123...n 5! = 12345 = 120

n k permutation 5P3 = 5! / (5-3)! = 60

n k combination 5C3 = 5!/[3!(5-3)!]=10

Set symbols

See also

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Math symbolsSet symbolsBasic math symbolsLogic symbolsGreek alphabet symbolsProbability distributionProbability & statistics

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