Tue. Jul 16th, 2019

Probability Symbols

Probability Symbols table

 

Symbol
Symbol Name
Meaning / definition
Example
P(A)
probability function
probability of event A
P(A) = 0.5
P(AB)
probability of events intersection
probability that of events A and B
P(AB) = 0.5
P(AB)
probability of events union
probability that of events A or B
P(AB) = 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
s2
sample variance
population samples variance estimator
s2 = 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) = λeλx , x≥0
gamma(c, λ)
gamma distribution
f (x) = λ c xc-1eλx / Γ(c), x≥0
χ 2(k)
chi-square distribution
f (x) = xk/2-1ex/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) = λkeλ / k!
Geom(p)
geometric distribution
f (k) = p(1-p) k
HG(N,K,n)
hyper-geometric 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
nPk
permutation
_{n}P_{k}=\frac{n!}{(n-k)!}
5P3 = 5! / (5-3)! = 60
nCk

combination
_{n}C_{k}=\binom{n}{k}=\frac{n!}{k!(n-k)!}
5C3 = 5!/[3!(5-3)!]=10