Business Statistics

220 Business Statistics

Binomial formula

Probability of x success in n trials = P(x) =

!

!( )!( )

x n x

n

p q

n x x

−

−

where p is the probability of success in any one trial, q the probability of failure in any one trial, n the number of trials, !n is (n) × (n – 1) ×

(n – 2) ×

...

× (2) × (1), and !0 = 1.

Mean and variance of a binomial probability distribution

Mean = m = E(x) = np

2

Var( ) (1 )x np p npq= = − =

Standard deviation =

npq=

Poisson formula

( )

!

−

×

=

x

e

P x

x

l

l

where P(x) is the probability of x occurrences in an interval, l the expected value or mean number of occurrence in an interval, and

e = 2.71828 (base of natural, logarithm ...