 # Probability And Statistics Symbols

Probability is the chance that something will happen – how likely it is that some event will happen. Statistics is the study of data: how to collect, summarize and present it. Probability and statistics are separate but two related academic disciplines. Statistical analysis often uses probability distributions, and the two topics are often studied together.

## List of Probability and Statistics Symbols

You can explore Probability and Statistics Symbols, name meanings and examples below-

##### 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(AB) = 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
$$\widetilde{x}$$ median middle value of random variable x $$\widetilde{x}= 5$$<
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 = (xx) / 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) = λeλx , 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/2-1ex/2 / ( 2k/2 Γ(k/2) )
Geom(p) geometric distribution f (k) =  p (1-p) k
Poisson(λ) Poisson distribution f (k) = λkeλ / k!
Bern(p) Bernoulli distribution
HG(N,K,n) hypergeometric distribution