# Probability Symbols

## Probability Symbols table

**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

σ

^{2}variance

variance of population values

σ

*= 4*^{2 }*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

*=2*_{X}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*

mid-range

*MR*= (

*x*+

_{max}*x*)/2

_{min}*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}*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*(

*k*

_{1}

*, k*

_{2})

F distribution

*Bin*(

*n*,

*p*)

binomial distribution

*f*(

*k*)

*=*(1

_{n}C_{k}p^{k}*-p*)

^{n-k}*Poisson*(λ)

Poisson distribution

*f*(

*k*)

*= λ*

^{k}e^{–λ}/

*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

_{n}P_{k}permutation

_{5}

*P*

_{3}

*=*5! / (5-3)! = 60

_{n}C_{k}combination

_{5}

*C*

_{3}

*=*5!/[3!(5-3)!]=10