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solving a system of two equations

• To: mathgroup at smc.vnet.net
• Subject: [mg101984] solving a system of two equations
• From: per <perfreem at gmail.com>
• Date: Sat, 25 Jul 2009 04:17:20 -0400 (EDT)

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.

• Follow-Ups:
  • Re: solving a system of two equations
    • From: DrMajorBob <btreat1@austin.rr.com>
  • Re: solving a system of two equations
    • From: Tomas Garza <tgarza10@msn.com>