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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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