| 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 |
| σ2 |
variance |
variance of population values |
σ2 = 4 |
| std(X) |
standard deviation |
standard deviation of random variable X |
std(X) = 2 |
| σX |
standard deviation |
standard deviation value of random variable X |
σX = 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 |
| ρX,Y |
correlation |
correlation of random variables X and Y |
ρX,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 |
mid-range |
MR = (xmax+xmin)/2 |
| Md |
sample median |
half the population is below this value |
| Q1 |
lower / first quartile |
25% of population are below this value |
| Q2 |
median / second quartile |
50% of population are below this value = median of samples |
| Q3 |
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 |
| zx |
standard score |
zx = (x-x) / sx |
| X ~ |
distribution of X |
distribution of random variable X |
X ~ N(0,3) |
| N(μ,σ2) |
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 xc-1e–λx / Γ(c), x≥0 |
| χ 2(k) |
chi-square distribution |
f (x) = xk/2-1e–x/2 / ( 2k/2 Γ(k/2) ) |
| F (k1, k2) |
F distribution |
| Bin(n,p) |
binomial distribution |
f (k) = nCk pk(1-p)n-k |
| Poisson(λ) |
Poisson distribution |
f (k) = λke–λ / k! |
| Geom(p) |
geometric distribution |
f (k) = p(1-p) k |
| HG(N,K,n) |
hyper-geometric distribution |
| Bern(p) |
Bernoulli distribution |