A sum problem

1. Apr 2, 2005

ArnfinnS

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. Apr 2, 2005

Zurtex

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

$$\frac{n \sum_{i=1}^{n} \left( X_i Y_i \right ) - \sum_{i=1}^{n} \left( X_i \right) \sum_{i=1}^{n} \left( Y_i \right) }{n \sum_{i=1}^{n} \left(X_i^2 \right) - \left( \sum_{i=1}^{n} X_i \right)^2}$$

And:

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

I've used x and y instead of X^ and Y^.

Last edited: Apr 2, 2005
3. Apr 2, 2005

ArnfinnS

hi

yes thats exactly what i meant:)
Can you help me?

4. Apr 2, 2005

ArnfinnS

hi

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

Can you help me?

5. Apr 2, 2005

Zurtex

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.

6. Apr 2, 2005

Data

Do you know what $x$ and $y$ 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: $x = \left(\sum_{i=0}^n X_i\right)/n$ and $y=\left(\sum_{i=0}^n Y_i \right)/n$

Last edited: Apr 2, 2005
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