# Probability and statistics symbols

Probability and statistics:
Probability is a measure of the likeliness that an event will occur.
Statistics is the study of the collection, organization, analysis, interpretation and presentation of data.It deals with all aspects of data including the planning of data collection in terms of the design of surveysand experiments. When analyzing data, it is possible to use one of two statistics methodologies:descriptive statistics or inferential statistics.

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(AB) = 0.5
P(A  B) probability of events union probability that of events A or B P(AB) = 0.5
P(A | B) conditional probability function probability of event A given event B occured P(A | B) = 0.3
(x) probability density function (pdf) P( x  b) = ∫ f (x)dx
F(x) cumulative distribution function (cdf) F(x) = P( 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 σ= 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 = (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
~ distribution of X distribution of random variable X ~ N(0,3)
N(μ,σ2) normal distribution gaussian distribution ~ N(0,3)
U(a,b) uniform distribution equal probability in range a,b ~ U(0,3)
exp(λ) exponential distribution (x) = λeλx , x≥0
gamma(c, λ) gamma distribution (x) = λ c xc-1eλx / Γ(c), x≥0
χ 2(k) chi-square distribution (x) = xk/2-1ex/2 / ( 2k/2 Γ(k/2) )
(k1, k2) F distribution
Bin(n,p) binomial distribution (k) = nCk pk(1-p)n-k
Poisson(λ) Poisson distribution (k) = λkeλ / k!
Geom(p) geometric distribution (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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