Re: solving a system of two equations
- To: mathgroup at smc.vnet.net
- Subject: [mg102002] Re: solving a system of two equations
- From: David Reiss <dbreiss at gmail.com>
- Date: Sun, 26 Jul 2009 03:54:51 -0400 (EDT)
- References: <h4ef1m$su0$1@smc.vnet.net>
In[46]:= Solve[{a/(a + b) ==
m, (a*b/((a + b)^2 (a + b + 1)) == v)}, {a, b}]
Out[46]= {{b -> (m - 2 m^2 + m^3 - v + m v)/v,
a -> (m^2 - m^3 - m v)/v}}
On Jul 25, 4:16 am, per <perfr... 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.