Re: A nasty 2x2 system of equations?

*To*: mathgroup at smc.vnet.net*Subject*: [mg54122] Re: A nasty 2x2 system of equations?*From*: Roland Franzius <roland.franzius at uos.de>*Date*: Fri, 11 Feb 2005 03:33:34 -0500 (EST)*Organization*: Universitaet Hannover*References*: <cuf559$glj$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Bruce Colletti wrote: > 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}] > << Statistics`ContinuousDistributions` X = BetaDistribution[a1, b1]; Y = BetaDistribution[a2, b2]; Z = BetaDistribution[a3, b3]; eq1 = Mean[Z] - c*Mean[X] - (1 - c)*Mean[Y] // Together // Numerator; eq2 = Variance[Z] - c^2*Variance[X] - (1 - c)^2*Variance[Y] // Together // Numerator; Solve[{eq1 == 0, eq2 == 0}, {a3, b3}]; but don't expect a useful expression except with real number input. -- Roland Franzius