       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>

```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.

--