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MathGroup Archive 2005

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Re: A nasty 2x2 system of equations?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg54121] Re: A nasty 2x2 system of equations?
  • From: "Carl K. Woll" <carlw at u.washington.edu>
  • Date: Fri, 11 Feb 2005 03:33:33 -0500 (EST)
  • Organization: University of Washington
  • References: <cuf559$glj$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Bruce,

I don't understand why Solve doesn't work here, but as a workaround you 
could try:

Solve[{Mean[Z] == m, Variance[Z] == v}, {a3, b3}] /. {m -> c*Mean[X] + (1 - 
c)*Mean[Y],
   v -> c^2*Variance[X] + (1 - c)^2*Variance[Y]}

Carl Woll

"Bruce Colletti" <vze269bv at verizon.net> wrote in message 
news:cuf559$glj$1 at smc.vnet.net...
> Re Mathematica 5.1.
>
> The code below keeps running without getting an answer.  Is the code 
> flawed or is this a really nasty system of 2-equations in 2-unknowns?
>
> Here's background:  X and Y are independent beta-distributed random 
> variables and Z is a convex combination of X and Y, i.e., Z = cX + (1 - 
> c)Y.
>
> Although Z need not be beta-distributed, let's pretend it is and in turn, 
> solve for its parms (a3 and b3) in terms of c and the known parms of X and 
> Y.
>
> Thanks.
>
> Bruce
>
> -------------
>
>
> X = BetaDistribution[a1, b1];
> Y = BetaDistribution[a2, b2];
> Z = BetaDistribution[a3, b3];
>
> Solve[{Mean[Z] == c*Mean[X] + (1 - c)*Mean[Y],
>   Variance[Z] == c^2*Variance[X] + (1 - c)^2*Variance[Y]}, {a3, b3}]
> 



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