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Math Help - Showing that one algebraic equation is equivalent to another (fairly complicated)

  1. #1
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    Showing that one algebraic equation is equivalent to another (fairly complicated)

    This is a part of a larger proof, which is irrelevant here. What I'm stuck on is showing that this:
    k*(u0-u)^2+n*(y-u)^2
    is the same as
    (k*n/(k+n))*(y-u0)^2+(k+n)*((k*u0+n*y)/(k+n)-u)^2

    Note that u0 and u are two different variables.

    I've been factoring and pushing things around for more than 2 hours. I'm embarrassed to be stuck
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  2. #2
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    Re: Showing that one algebraic equation is equivalent to another (fairly complicated)

    Quote Originally Posted by birdz View Post
    This is a part of a larger proof, which is irrelevant here. What I'm stuck on is showing that this:
    k*(u0-u)^2+n*(y-u)^2
    is the same as
    (k*n/(k+n))*(y-u0)^2+(k+n)*((k*u0+n*y)/(k+n)-u)^2

    Note that u0 and u are two different variables.

    I've been factoring and pushing things around for more than 2 hours. I'm embarrassed to be stuck
    \frac{kn}{k+n} \cdot (y-u_0)^2 + (k+n) \cdot \left(\frac{ku_0+ny-ku-nu}{k+n}\right)^2=

     = \frac{kn(y-u_0)^2}{k+n}+\frac{(ku_0+ny-ku-nu)^2}{k+n} =

     = \frac{kn(y-u_0)^2+(k(u_0-u)+n(y-u))^2}{k+n}

    I think that you can proceed from here....
    Thanks from birdz
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  3. #3
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    Re: Showing that one algebraic equation is equivalent to another (fairly complicated)

    Quote Originally Posted by birdz View Post
    Note that u0 and u are two different variables.
    Why not use v? Easier to "handle" than u0, like less possible confusion...
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  4. #4
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    Re: Showing that one algebraic equation is equivalent to another (fairly complicated)

    princeps- Thank you so much!!!

    Quote Originally Posted by Wilmer View Post
    Why not use v? Easier to "handle" than u0, like less possible confusion...
    You're right I probably should have. Although it's a bit easier for me to use notation similar to my original variables (selfish, I know). 'u' refers to the "true mean" and 'u0' refers to the mean of the prior. It's from the process of updating the prior of a normal-inverse chi squared distribution.
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  5. #5
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    Re: Showing that one algebraic equation is equivalent to another (fairly complicated)

    Whatever turns you on...
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