# 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