       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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