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Probability and statistics symbols

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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

http://www.rapidtables.com/math/symbols/statistical_symbols/median.GIF

median

middle value of random variable x

http://www.rapidtables.com/math/symbols/statistical_symbols/median_ex.GIF

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

http://www.rapidtables.com/math/symbols/statistical_symbols/sum_ex.gif

∑∑

double summation

double summation

http://www.rapidtables.com/math/symbols/statistical_symbols/double_sum_ex.gif

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

 

 

 

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