Probability And Statistics Symbols

Symbol	Symbol Name	Meaning /  definition	Example
P(A ∩ B)	probability of events intersection	probability that of events A and B	P(A∩B) = 0.5
P(A)	probability function	probability of event A	P(A) = 0.5
P(A | B)	conditional probability function	probability of event A given event B occurred	P(A | B) = 0.3
P(A ∪ B)	probability of events union	probability that of events A or B	P(A∪B) = 0.5
F(x)	cumulative distribution function (cdf)	F(x) = P(X ≤ x)
f (x)	probability density function (pdf)	P(a ≤ x ≤ b) = ∫ f (x) dx
E(X)	expectation value	expected value of random variable X	E(X) = 10
μ	population mean	mean of population values	μ = 10
var(X)	variance	variance of random variable X	var(X) = 4
E(X | Y)	conditional expectation	expected value of random variable X given Y	E(X | Y=2) = 5
std(X)	standard deviation	standard deviation of random variable X	std(X) = 2
σ2	variance	variance of population values	σ2 = 4
˜x	median	middle value of random variable x	˜x=5
σX	standard deviation	standard deviation value of random variable X	σX  = 2
corr(X,Y)	correlation	correlation of random variables X and Y	corr(X,Y) = 0.6
cov(X,Y)	covariance	covariance of random variables X and Y	cov(X,Y) = 4
ρX,Y	correlation	correlation of random variables X and Y	ρX,Y = 0.6
Mo	mode	value that occurs most frequently in population
Md	sample median	half the population is below this value
MR	mid-range	MR = (xmax+xmin)/2
Q2	median / second quartile	50% of population are below this value = median of samples
Q1	lower / first quartile	25% of population are below this value
x	sample mean	average / arithmetic mean	x = (2+5+9) / 3 = 5.333
Q3	upper / third quartile	75% of population are below this value
s	sample standard deviation	population samples standard deviation estimator	s = 2
s 2	sample variance	population samples variance estimator	s 2 = 4
X ~	distribution of X	distribution of random variable X	X ~ N(0,3)
zx	standard score	zx = (x–x) / sx
U(a,b)	uniform distribution	equal probability in range a,b	X ~ U(0,3)
N(μ,σ2)	normal distribution	gaussian distribution	X ~ N(0,3)
gamma(c, λ)	gamma distribution	f (x) = λ c xc-1e-λx / Γ(c), x≥0
exp(λ)	exponential distribution	f (x) = λe–λx , x≥0
F (k1, k2)	F distribution
Bin(n,p)	binomial distribution	f (k) = nCk pk(1-p)n-k
χ 2(k)	chi-square distribution	f (x) = xk/2-1e–x/2 / ( 2k/2 Γ(k/2) )
Geom(p)	geometric distribution	f (k) =  p (1-p) k
Poisson(λ)	Poisson distribution	f (k) = λke–λ / k!
Bern(p)	Bernoulli distribution
HG(N,K,n)	hypergeometric distribution