Re: solving a system of two equations

*To*: mathgroup at smc.vnet.net*Subject*: [mg102014] Re: solving a system of two equations*From*: Helen Read <hpr at together.net>*Date*: Sun, 26 Jul 2009 03:57:03 -0400 (EDT)*References*: <h4ef1m$su0$1@smc.vnet.net>*Reply-to*: HPR <read at math.uvm.edu>

per 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? Tell it to solve for both a and b and all is well. Solve[{a/(a + b) == 1/2, a*b/((a + b)^2 (a + b + 1)) == 2}, {a, b}] Also I'd suggest entering 1/2 in your first equation, not 0.5, in order to find exact solutions. -- Helen Read University of Vermont

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

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

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