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 

