Re: Expected value of the Geometric distribution
- To: mathgroup at smc.vnet.net
- Subject: [mg118459] Re: Expected value of the Geometric distribution
- From: Daniel Lichtblau <danl at wolfram.com>
- Date: Fri, 29 Apr 2011 07:29:18 -0400 (EDT)
Tonja Krueger wrote: > Hi all, > I want to calculate expected value of diverse distributions like the Geometric distribution (for example). > As I understand this, the expected value is the integral of the density function *x. > But when I try to calculate this: > Integrate[(1-p)^k*p*k,k] > I get this as the answer: > ((1 - p)^k p (-1 + k Log[1 - p]))/Log[1 - p]^2 > Instead of: (1-p)/p. > I would be so grateful if someone could explain to me what I'm doing wrong. > Tonja > ___________________________________________________________ > Empfehlen Sie WEB.DE DSL Ihren Freunden und Bekannten und wir > belohnen Sie mit bis zu 50,- Euro! https://freundschaftswerbung.web.de > There are two issues here. (1) This is a discrete distribution. So you will want a sum rather than an integral. (2) To obtain an expectation one uses a definite rather than indefinite "integral" (discrete sum in this case, but that is a type of integral in mathematics). Sum[(1-p)^k*p*k, {k,0,Infinity}] // InputForm Out[128]//InputForm= (1 - p)/p Daniel Lichtblau Wolfram Research