Probability and statistics symbols table and definitions.
Probability and statistics symbols table
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 |
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 |
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 |
ρX,Y | correlation | correlation of random variables X and Y | ρX,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 = (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 |
Combinatorics Symbols
Symbol | Symbol Name | Meaning / definition | Example |
---|---|---|---|
n! | factorial | n! = 1⋅2⋅3⋅...⋅n | 5! = 1⋅2⋅3⋅4⋅5 = 120 |
nPk | permutation | 5P3 = 5! / (5-3)! = 60 | |
nCk
|
combination | 5C3 = 5!/[3!(5-3)!]=10 |
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