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This module provides an overview of Statistics Formulas used as a part of Collaborative Statistics collection (col10522) by Barbara Illowsky and Susan Dean.
Formula

Factorial

n ! = n ( n 1 ) ( n 2 ) . . . ( 1 )

0 ! = 1

Formula

Combinations

n r = n ! ( n r ) ! r !

Formula

Binomial distribution

X ~ B ( n , p )

P ( X = x ) = n x p x q n x , for x = 0 , 1 , 2 , . . . , n

Formula

Geometric distribution

X ~ G ( p )

P ( X = x ) = q x 1 p , for x = 1 , 2 , 3 , . . .

Formula

Hypergeometric distribution

X~H ( r , b , n )

P ( X = x ) = ( ( r x ) ( b n x ) ( r + b n ) )

Formula

Poisson distribution

X~P ( μ )

P ( X = x ) = μ x e μ x !

Formula

Uniform distribution

X ~ U ( a , b )

f ( X ) = 1 b a , a < x < b

Formula

Exponential distribution

X ~ Exp ( m )

f ( x ) = m e mx , m > 0 , x 0

Formula

Normal distribution

X ~ N ( μ , σ 2 )

f ( x ) = 1 σ 2 π e ( x μ ) 2 2 σ 2 , - < x <

Formula

Gamma function

Γ ( z ) = 0 x z 1 e x dx z > 0

Γ ( 1 2 ) = π

Γ ( m + 1 ) = m ! for m , a nonnegative integer

otherwise: Γ ( a + 1 ) = ( a )

Formula

Student-t distribution

X ~ t df

f ( x ) = ( 1 + x 2 n ) ( n + 1 ) 2 Γ ( n + 1 2 ) Γ ( n 2 )

X = Z Y n

Z ~ N ( 0,1 ) , Y ~ Χ df 2 , n = degrees of freedom

Formula

Chi-square distribution

X ~ Χ df 2

f ( x ) = x n 2 2 e x 2 2 n 2 Γ ( n 2 ) , x > 0 , n = positive integer and degrees of freedom

Formula

F distribution

X ~ F df ( n ) , df ( d )

df ( n ) = degrees of freedom for the numerator

df ( d ) = degrees of freedom for the denominator

f ( x ) = Γ ( u + v 2 ) Γ ( u 2 ) Γ ( v 2 ) ( u v ) u 2 x ( u 2 1 ) [ 1 + ( u v ) x . 5 ( u + v ) ]

X = Y u W v , Y , W are chi-square

Questions & Answers

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Source:  OpenStax, Collaborative statistics. OpenStax CNX. Jul 03, 2012 Download for free at http://cnx.org/content/col10522/1.40
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