Discrete Distributions

0.3

0.31

0.45

0.45 0.02 0.68 1 0.25

0 0.02

S. No.

BINOMIAL

HYPERGEOMETRIC

POISSON

GEOMETRIC

Parameters

n, p n = total no. of trials p = prob. Of success x = successsful no. of trial

n, N, D n = Sample size N = Population size D = No. of successful events in population

µ µ = Avg. no. of events within a unit.

p p = Success rate of single trial x = trials to obtain st susscess

BINOMDIST(x,n,p,0) when x=2

HYPGEOMDIST(x,n,D,N) when x=3 No cumulative excel func.

POISSON(x,µ,0) when x=2

P(x,p) = p(1-p)^(x-1)

BINOMDIST(x,n,p,1) when x<=2

P(X≤5) = P(X=0,1,2,3,4,5)

POISSON(x,µ,1) when x<=2

P(x>n) = (1-p)^n

P(X>2) = 1- P(X≤2)

P(X>2) = 1- P(X=0,1,2)

P(X>2) = 1- P(X≤2)

P(X≤2) = 1- P(X>2)

P(X≥8) = 1- P(X≤7)

P(X≥5) = 1- P(X=0,1,2,3,4)

P(X≥8) = 1- P(X≤7)

P(X≥8) = P(X>7)

P(X<9) = P(X≤8)

P(X<2) = P(X=0,1)

P(X<9) = P(X≤8)

P(X<9) = P(X≤8) = 1- P(X>8)

Mean

µ = np

µ = n*(D/N)

µ

µ = 1/p

Variance

var = np*(1-p)

var = n(D/N)*(1-(D/N))*(N-n/N-1)

µ

var = (1-p)/p2

Formula