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A nasty 2x2 system of equations?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg54098] A nasty 2x2 system of equations?
*From*: Bruce Colletti <vze269bv at verizon.net>
*Date*: Thu, 10 Feb 2005 02:47:14 -0500 (EST)
*Sender*: owner-wri-mathgroup at wolfram.com
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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