Statistical Symbols

Statistical Symbols

Probability and statistics symbols table and definitions.

Probability and statistics symbols table

Symbol

P(A)

P(A ∩ B)

P(A ∪ B)

P(A | B)

f (x)

F(x)

μ

E(X)

E(X | Y)

var(X)

σ²

std(X)

σ_X

Symbol Name

probability function

probability of events intersection

probability of events union

conditional probability function

probability density function (pdf)

cumulative distribution function (cdf)

population mean

expectation value

conditional expectation

standard deviation

standard deviation

median

covariance

correlation

correlation

summation

double summation

mode

mid-range

sample median

lower / first quartile

median / second quartile

upper / third quartile

sample mean

sample variance

sample standard deviation

standard score

distribution of X

normal distribution

uniform distribution

exponential distribution

gamma distribution

chi-square distribution

F distribution

binomial distribution

Poisson distribution

geometric distribution

hyper-geometric distribution

Bernoulli distribution

Meaning / definition

probability of event A

probability that of events A and B

probability that of events A or B

probability of event A given event B occured

P(a ≤ x ≤ b) = ∫ f (x) dx

F(x) = P(X ≤ x)

mean of population values

expected value of random variable X

expected value of random variable X given Y

variance of random variable X

variance of population values

standard deviation of random variable X

standard deviation value of random variable X

middle value of random variable x

covariance of random variables X and Y

correlation of random variables X and Y

correlation of random variables X and Y

summation - sum of all values in range of series

double summation

value that occurs most frequently in population

Example

P(A) = 0.5

P(A∩B) = 0.5

P(A∪B) = 0.5

P(A | B) = 0.3

μ = 10

E(X) = 10

E(X | Y=2) = 5

var(X) = 4

σ²= 4

std(X) = 2

σ_X= 2

cov(X,Y)

corr(X,Y)

ρ_X_,Y

∑

∑∑

Mo

MR

Md

Q₁

Q₂

Q₃

x

s²

s

z_x

X ~

N(μ,σ²)

U(a,b)

exp(λ)

gamma(c, λ)

χ²(k)

F (k₁, k₂)

Bin(n,p)

Poisson(λ)

Geom(p)

HG(N,K,n)

Bern(p)

cov(X,Y) = 4

corr(X,Y) = 0.6

ρ_X_,Y = 0.6

MR = (x_max+x_min)/2

x = (2+5+9) / 3 = 5.333

s² = 4

s = 2

X ~ N(0,3)

X ~ N(0,3)

X ~ U(0,3)

half the population is below this value

25% of population are below this value

50% of population are below this value = median of samples

75% of population are below this value

average / arithmetic mean

population samples variance estimator

population samples standard deviation estimator

z_x = (x-x) / s_x

distribution of random variable X

gaussian distribution

equal probability in range a,b

f (x) = λe^-λx , x≥0

f (x) = λ c x^c-1e^-λx / Γ(c),x≥0

f (x) = x^k^/2-1e^-x/2 / ( 2^k/2Γ(k/2) )

f (k) = _nC_k p^k(1-p)^n-k

f (k) = λ^ke^-λ / k!

f (k) = p(1-p)^k

Combinatorics Symbols

Symbol

n!

_nP_k

_nC_k

Symbol Name

permutation

combination

Meaning / definition

n! = 1·2·3·...·n

Example

5! = 1·2·3·4·5 = 120

₅P₃ = 5! / (5-3)! = 60

₅C₃ = 5!/[3!(5-3)!]=10

$_{n}P_{k}=\frac{n!}{(n-k)!}$

$_{n}C_{k}=\binom{n}{k}=\frac{n!}{k!(n-k)!}$

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