Geometric Distributions

Below is my Google Docs Spreadsheet for Geometric Distributions:

This sheet you cannot change because I have it locked, but if you would like access so you can use my sheet, and just put in your data and get the answer - email me: messenger1964@yahoo.com

	Geometric Distribution
		x	p	Answer
	Formula	0	0.25
	p(x) = p(1-p)^(x) =	-->	-->	0.25
	where p is the probability of success, 0<p<1 and x = {0,1,2.....}
	Google Sheets Function
	[=NEGBINOMDIST(x,1,p)]	-->	-->	0.25
	(more google sheets functions - see below)
	Mean
	E[X]=μ = (1-p)/p
	μ =	-->	-->	3
	Variance
	Var = σ^(2)
	σ^(2) = (1-p)/p^(2)
	σ^(2)=	-->	-->	12
	Standard Deviation
	St.Dev = √σ	-->	-->	3.46410161513775
	Third Moment of X about the Mean =
	E[(X-E[X])^(3)]=
	(1-p)*(2-p)/p^(3)=	-->	-->	84
	4th Moment of X about the Mean =
	E[(X-E[X])^(4)]=
	(1-p)*(p^(2)-9p+9)/p^(4)=	-->	-->	1308
	Moment Generating Function
	M(t) = E[e^(tX)] = p*(1/((1-e^(t))*(1-p))
	p*(1/((1-e^(t))*(1-p))
	Distribution Function
	∀t < 0 ......F(t) = P{X≤t} =P{X∉R} = 0
	∀t ≥ 0 ......F(t) = P{X≤[t]} = 1-(1-p)^([t]+1)
	Google Sheets Function (All)
	BINOMDIST(num_successes, num_trials, prob_success, cumulative)
	P{X=x} [=NEGBINOMDIST(x,1,p)]
	P{X≤x} [=NEGBINOMDIST(x,1,p)]
	P{X<x} [=NEGBINOMDIST(x,1,p)]
	P{X>x} [=1-NEGBINOMDIST(x,1,p)]
	P{X≥x} [=1-NEGBINOMDIST(x-1,1,p)]
	x<y
	P{x<X<y} [=NEGBINOMDIST(y-1,1,p)-[=NEGBINOMDIST(x,1,p)]
	P{x<X≤y} [=NEGBINOMDIST(y,1,p)-[=NEGBINOMDIST(x,1,p)]
	P{x≤X<y} [=NEGBINOMDIST(y-1,1,p)-[=NEGBINOMDIST(x-1,1,p)]
	P{x≤X≤y} [=NEGBINOMDIST(y,1,p)-[=NEGBINOMDIST(x-1,1,p)]
	http://mathworld.wolfram.com/GeometricDistribution.html
	http://www.math.uah.edu/stat/bernoulli/Geometric.html
	http://en.wikipedia.org/wiki/Geometric_distribution#Moments_and_cumulants