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 
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  midrange  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} = (xx) / 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^{c1}e^{λx} / Γ(c), x≥0  
χ^{ 2}(k)  chisquare distribution  f (x) = x^{k}^{/21}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}(1p)^{nk}  
Poisson(λ)  Poisson distribution  f (k) = λ^{k}e^{λ} / k!  
Geom(p)  geometric distribution  f (k) = p(1p)^{ k}  
HG(N,K,n)  hypergeometric 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 
_{n}P_{k}  permutation  _{5}P_{3} = 5! / (53)! = 60  
_{n}C_{k}

combination  _{5}C_{3} = 5!/[3!(53)!]=10 
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