       Re: solving a system of two equations

• To: mathgroup at smc.vnet.net
• Subject: [mg102008] Re: [mg101984] solving a system of two equations
• From: Tomas Garza <tgarza10 at msn.com>
• Date: Sun, 26 Jul 2009 03:55:57 -0400 (EDT)
• References: <200907250817.EAA29655@smc.vnet.net>

```Try this (I guess you forgot to write the second variable, b, in the NSolve statement):

In:= sol = NSolve[{a/(a+b)==0.5,
a*b/((a+b)^2 (a+b+1))==2},{a,b}]

Out= {{a->-0.4375,b->-0.4375}}

Check:

In:= a/(a+b)/.sol

Out= {0.5}

In:= a*b/((a+b)^2 (a+b+1))/.sol

Out= {2.}

In this case it's better to use NSolve rather than Solve.

Tomas

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

```

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