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A sum problem

  1. Apr 2, 2005 #1
    hi i have a small problem.
    i need to prove that these two expressions are equal :

    (n*Sum{i=1,n}Xi*Yi - Sum{i=1,n}Xi*Sum{i=1,n}Yi)/(n*Sum{i=1,n}(Xi)^2 - (Sum{i=1,n}Xi)^2)

    and the expression :

    (Sum{i=1,n}(Xi)*(Xi*Y^ - Yi*X^))/(Sum{i=1,n}((Xi)^2 - (x^)^2 ))

    here is x^ and y^ the middle values of x and y .

    i need to transpose the one expression over in the other. But i cant get this to work.

    Can someone help me?
     
  2. jcsd
  3. Apr 2, 2005 #2

    Zurtex

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    Eek, these come off as very confusing, it would really help if you could learn LaTeX, did you mean:

    [tex]\frac{n \sum_{i=1}^{n} \left( X_i Y_i \right ) - \sum_{i=1}^{n} \left( X_i \right) \sum_{i=1}^{n} \left( Y_i \right) }{n \sum_{i=1}^{n} \left(X_i^2 \right) - \left( \sum_{i=1}^{n} X_i \right)^2}[/tex]

    And:

    [tex]\frac{\sum_{i=1}^{n} \left( X_i \left(X_iy - Y_ix \right) \right)}{\sum_{i=1}^{n} \left( \left X_i^2 - x^2 \right)} [/tex]

    I've used x and y instead of X^ and Y^.
     
    Last edited: Apr 2, 2005
  4. Apr 2, 2005 #3
    hi

    yes thats exactly what i meant:)
    Can you help me?
     
  5. Apr 2, 2005 #4
    hi

    yes thats exactly what i meant:) I need to transform the one expression over in the other.

    Can you help me?
     
  6. Apr 2, 2005 #5

    Zurtex

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    Actually I made a slight mistake in representing the 2nd one, I think that's waht you mean now. Sorry I have no idea how to do this, just putting it in clear form for those who might.
     
  7. Apr 2, 2005 #6
    Do you know what [itex]x[/itex] and [itex]y[/itex] mean in terms of things from the first expression?

    edit: nevermind, it seems that you've said something in your first post. I take it you mean they're the averages? in that case here's a hint: [itex] x = \left(\sum_{i=0}^n X_i\right)/n[/itex] and [itex]y=\left(\sum_{i=0}^n Y_i \right)/n[/itex]
     
    Last edited: Apr 2, 2005
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