| Symbol |
Symbol Name |
Meaning/Definition |
Example |
| \( P(A) \) |
probability function |
probability of event A |
\( P(A) = 0.5 \) |
| \( P(A \cap B) \) |
probability of events intersection |
probability that of events A and B |
\( P(A\cap B) = 0.5 \) |
| \( P(A \cup B) \) |
probability of events union |
probability that of events A or B |
\( P(A\cup B) = 0.5 \) |
| \( P(A | B) \) |
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 |
\( σ_X = 2 \) |
| \( \tilde {x} \) |
median |
middle value of random variable x |
\( \tilde {x} = 5 \) |
| \( cov(X,Y) \) |
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 |
\( ρ_{X,Y}=0.6 \) |
| \( Mo \) |
mode |
value that occurs most frequently in population |
\( \) |
| \( MR \) |
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 |
\( z_x = (x-x) / s_x \) |
|
| \( X ~ \) |
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 |
\( f (x) = λ c x^{c-1}e^{-λx} / Γ(c), x≥0 \) |
|
| \( χ^2(k) \) |
chi-square distribution |
\( f (x) = x^{k/2-1}e^{-x/2} / ( 2^{k/2} Γ(k/2) ) \) |
|
| \( F (k1, k2) \) |
F distribution |
|
\( \) |
| \( Bin(n,p) \) |
binomial distribution |
\( f (k) = ^nC_k p^k(1-p)^{n-k} \) |
|
| \( Poisson(λ) \) |
Poisson distribution |
\( f (k) = λ^ke^{-λ} / k! \) |
|
| \( Geom(p) \) |
geometric distribution |
\( f (k) = p(1-p)^k \) |
|
| \( HG(N,K,n) \) |
hyper-geometric distribution |
|
\( \) |
| \( Bern(p) \) |
Bernoulli distribution |
|
\( \) |
