Re: solving a system of two equations

*To*: mathgroup at smc.vnet.net*Subject*: [mg102012] Re: [mg101984] solving a system of two equations*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Sun, 26 Jul 2009 03:56:41 -0400 (EDT)*Reply-to*: hanlonr at cox.net

Solve is intended for linear and polynomial equations (see Help). Reduce is much more general. Reduce[{a/(a + b) == 1/2, a*b/((a + b)^2 (a + b + 1)) == 2}, a] // ToRules {b -> -(7/16), a -> -(7/16)} Bob Hanlon ---- per <perfreem at gmail.com> wrote: ============= hi all, i am trying to find two parameters a, b of the Beta distribution that make its mean equal to some given constant m and its variance equal to some given constant v. this reduces to solving a system of two equations based on the mean/variance definitions of the beta distribution: a/(a+b) = m a*b/((a + b)^2 (a + b + 1)) = v i want to solve this equation for a and b. i tried to solve this in mathematica, as follows (for m = .5, v = 1): Solve[{a/(a + b) == .5, a*b/((a + b)^2 (a + b + 1)) == 2}, a] But it returns: {} i want to get back values for a and b. does anyone know how i can do this? also, this is subject to the constraint that a and b are positive real numbers but i am not sure how to express that. thank you.

**Re: solving a system of two equations**

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**Re: solving a system of two equations**

**Re: solving a system of two equations**