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.
You can explore Probability and Statistics Symbol’s, names meanings and examples below
Symbol  Symbol Name  Meaning / definition  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(A∪B) = 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 
σ^{2}  variance  variance of population values  σ^{2 }= 4 
\(\widetilde{x}\)  median  middle value of random variable x  \(\widetilde{x}= 5\)< 
σ_{X}  standard deviation  standard deviation value of random variable X  σ_{X}_{ }= 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 
ρ_{X}_{,Y}  correlation  correlation of random variables X and Y  ρ_{X}_{,Y} = 0.6 
Mo  mode  value that occurs most frequently in population  
Md  sample median  half the population is below this value  
MR  midrange  MR = (x_{max}+x_{min})/2  
Q2  median / second quartile  50% of population are below this value = median of samples  
Q_{1}  lower / first quartile  25% of population are below this value  
x  sample mean  average / arithmetic mean  x = (2+5+9) / 3 = 5.333 
Q_{3}  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) 
z_{x}  standard score  z_{x} = (x–x) / s_{x}  
U(a,b)  uniform distribution  equal probability in range a,b  X ~ U(0,3) 
N(μ,σ^{2})  normal distribution  gaussian distribution  X ~ N(0,3) 
gamma(c, λ)  gamma distribution  f (x) = λ c xc1eλx / Γ(c), x≥0  
exp(λ)  exponential distribution  f (x) = λe^{–λx} , x≥0  
F (k1, k2)  F distribution  
Bin(n,p)  binomial distribution  f (k) = nCk pk(1p)nk  
χ^{ 2}(k)  chisquare distribution  f (x) = x^{k}^{/21}e^{–x/2} / ( 2^{k/2 }Γ(k/2) )  
Geom(p)  geometric distribution  f (k) = p (1p) k  
Poisson(λ)  Poisson distribution  f (k) = λ^{k}e^{–λ} / k!  
Bern(p)  Bernoulli distribution  
HG(N,K,n)  hypergeometric distribution 
