Results 1 to 4 of 4

Math Help - transforming one equation into another

  1. #1
    Member
    Joined
    May 2012
    From
    Toronto
    Posts
    244
    Thanks
    1

    transforming one equation into another

    if I have \frac {x}{n}  + x - \frac{n}{n-1} how can I transform it into x  + nx - \frac{n}{n-1}?


    I can't seem to do it without changing the n/(n-1) term into n^2/(n-1)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2010
    Posts
    1,845
    Thanks
    715

    Re: transforming one equation into another

    Please give the whole problem. The expression \dfrac{x}{n}+x - \dfrac{n}{n-1} is a different expression from x+nx - \dfrac{n}{n-1}. I would need the full context to be able to help further.

    If \dfrac{x}{n} + x - \dfrac{n}{n-1} = 0 then x + nx - \dfrac{n^2}{n-1} = 0 as you suggested. Or, \dfrac{x}{n} + x - \dfrac{n}{n-1} = \dfrac{1}{n}(x + nx) - \dfrac{n}{n-1}. Without more information, I don't know how to help you.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    May 2012
    From
    Toronto
    Posts
    244
    Thanks
    1

    Re: transforming one equation into another

    sorry about that. It's a statistics problem that becomes an algebra problem.

    I have as an estimator of the variance of the population  \frac{\sum(y_i - \bar{y})^2}{n} - \frac{n}{n-1} + \sum(y_i - \bar{y})^2 and I'm trying to find out if it's biased or not, meaning if I take the expectation whether or not the expression remains the same. When I take the expectation I get

    \sum(y_i - \bar{y})^2 - \frac{n}{n-1} + n \sum(y_i - \bar{y})^2 (I hope that's right, if not the whole thing here is wrong) and the question is how would I make this unbiased, which I interpret to mean that I have to find some way of algebraically making the second statement equivalent to the first. In the above problem I let E( \sum (y_i - \bar{y})^2 )= VARIANCE(Y) = x so as to simplify the algebra.

    It could be that my statistics up to this point are wrong and perhaps this is why the algebra is not working.
    Last edited by kingsolomonsgrave; November 5th 2013 at 05:14 AM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Nov 2010
    Posts
    1,845
    Thanks
    715

    Re: transforming one equation into another

    Ahh, my knowledge of statistics is rather limited. But, would this help with the algebra? Rewriting your original expression, you have

    \dfrac{\sum{(y_i-\overline{y})^2}}{n} - \dfrac{n}{n-1} + \sum{(y_i - \overline{y})^2} = \dfrac{n+1}{n}\sum{(y_i - \overline{y})^2} - \dfrac{n}{n-1}

    If you find the expected value of the RHS expression, do you get (n+1)\sum(y_i-\overline{y})^2 - \dfrac{n}{n-1}? If so, then your algebra looks correct to me, and maybe the estimator is biased.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Equation of graph after transforming
    Posted in the Algebra Forum
    Replies: 3
    Last Post: October 18th 2011, 04:18 PM
  2. Replies: 5
    Last Post: September 21st 2011, 12:12 AM
  3. Replies: 4
    Last Post: May 8th 2011, 12:27 PM
  4. Replies: 1
    Last Post: October 9th 2007, 06:10 PM
  5. Transforming Formulas
    Posted in the Algebra Forum
    Replies: 1
    Last Post: March 7th 2007, 11:12 PM

Search Tags


/mathhelpforum @mathhelpforum