Probability & Statistics Symbols – List of all probability & statistics symbols and signs – meaning and examples.
Symbol | Symbol Name | Meaning / definition | Example |
---|---|---|---|
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) | |
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 |
σ^{2} | variance | variance of population values | σ^{2 }= 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 |
ρ_{X,Y} | 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 | |
Mo | mode | value that occurs most frequently in population | |
MR | mid-range | MR = (x_{max}+x_{min})/2 | |
Md | sample median | half the population is below this value | |
Q_{1} | lower / first quartile | 25% of population are below this value | |
Q_{2} | median / second quartile | 50% of population are below this value = median of samples | |
Q_{3} | 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 |
z_{x} | standard score | z_{x} = (x–x) / s_{x} | |
X ~ | distribution of X | distribution of random variable X | X ~ N(0,3) |
N(μ,σ^{2}) | 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-1}e^{–λx }/ Γ(c), x≥0 | |
χ^{ 2}(k) | chi-square distribution | f (x) = x^{k}^{/2-1}e^{–x/2 }/ ( 2^{k/2 }Γ(k/2) ) | |
F (k_{1}, k_{2}) | F distribution | ||
Bin(n,p) | binomial distribution | f (k) = _{n}C_{k }p^{k}(1-p)^{n-k} | |
Poisson(λ) | Poisson distribution | f (k) = λ^{k}e^{–λ }/ k! | |
Geom(p) | geometric distribution | f (k) = p (1-p)^{ k} | |
HG(N,K,n) | hyper-geometric distribution | ||
Bern(p) | Bernoulli distribution |