Mathematica 9 is now available
Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2004
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2004

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Binomial ratio expectation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg49936] Re: [mg49905] Binomial ratio expectation
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Fri, 6 Aug 2004 03:10:09 -0400 (EDT)
  • Reply-to: hanlonr at cox.net
  • Sender: owner-wri-mathgroup at wolfram.com

Needs["Statistics`DiscreteDistributions`"];

dist=BinomialDistribution[n, w];

ev=FullSimplify[ExpectedValue[x/(2+x), dist,x], 0<=w<=1]

(-2*(w - 2)*w*(1 - w)^n - 2*(1 - w)^n + 
   (n + 2)*w*(n*w + w - 2) + 2)/((n + 1)*(n + 2)*w^2)

Limit[ev , w->0]

0

ev /. w -> 1 // Simplify

n/(n + 2)

ev == FullSimplify[Sum[x/(x+2)*PDF[dist,x], {
      x,0,n}], 0<=w<=1]

True


Bob Hanlon

> 
> From: Ismo Horppu <ishorppu at NOSPAMitu.st.jyu.fi>
To: mathgroup at smc.vnet.net
> Date: 2004/08/05 Thu AM 09:22:25 EDT
> To: mathgroup at smc.vnet.net
> Subject: [mg49936] [mg49905] Binomial ratio expectation
> 
> I have the following problem, I need to compute 
> EXPECTATION[X/(2+X)], 
> where X follows Binomial distribution with n trials and success 
> probability of w.
> 
> I have tried to solve it with Mathematica (version 4.1) as
> Sum[((x)/(2 + x))*Binomial[n, x]*w^x*(1 - w)^(n - x), {x, 0, n}]
> 
> I omit here the result which seems to be okay (according to 
> simulations) for values 0<w<1. Problem is that result (intermediate 
> or full simplified one) is not defined with values 0 or 1 of parameter w.
> However, it is trivial to compute the result by hand on those cases 
> (as the X is then a fixed constant, 0 or n). 
> 
> Does anyone know how to get the full result with Mathematica, or at 
> least a warning that the result is partial. I am also interested in 
> whether someone knows what kind of summation formula Mathematica 
uses 
> for the sum, some kind of binomial identity formula perhaps? (I am 
> unable to find which one, any references would be appreciated).
> 


  • Prev by Date: Re: Binomial ratio expectation
  • Next by Date: Re: populate a list with random numbers from normaldistribution?
  • Previous by thread: Re: Binomial ratio expectation
  • Next by thread: Re: Binomial ratio expectation