Probability Symbols

P(A)

probability function

probability of event A

P(A) = 0.5

P(A ∩ B)

probability of events intersection

probability that of events A and B

P(A∩B) = 0.5

P(A ∪ B)

probability of events union

probability that of events A or B

P(A∪B) = 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)

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

σ_X

standard deviation

standard deviation value of random variable X

σ_X=2

median

middle value of random variable x

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

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

mode

value that occurs most frequently in population

mid-range

MR = (x_max+x_min)/2

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

sample mean

average / arithmetic mean

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

sample variance

population samples variance estimator

s² = 4

sample standard deviation

population samples standard deviation estimator

s = 2

standard score

z_x = (x-x) / s_x

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 x^c-1e^–λx / Γ(c), x≥0

χ ²(k)

chi-square distribution

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

F (k₁, k₂)

F distribution

Bin(n,p)

binomial distribution

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

Poisson(λ)

Poisson distribution

f (k) = λ^ke^–λ / k!

Geom(p)

geometric distribution

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

HG(N,K,n)

hyper-geometric distribution

Bern(p)

Bernoulli distribution

n!

factorial

n! = 1·2·3·…·n

5! = 1·2·3·4·5 = 120

permutation

₅P₃ = 5! / (5-3)! = 60

_nC_k

combination

₅C₃ = 5!/[3!(5-3)!]=10