Proof that's missing a step

1. Nov 27, 2011

ƒ(x)

1. The problem statement, all variables and given/known data

Show that

c(0) = $\sigma$$^{2}$

2. Relevant equations

c($\ell$) = $\frac{1}{N-\ell}$ $\sum$ y$_{i}$y$_{i+\ell}$, with the summation going from i=1 to N-$\ell$

y(i) = x(i)-$\langle$x$\rangle$

$\langle$x$\rangle$=$\frac{1}{N}$$\sum$x(i)

$\langle$x2$\rangle$=$\frac{1}{N}$$\sum$x(i)2

Edit: the other summations go from 1 to N

Edit: forgot sigma

$\sigma$2 = ($\langle$x2$\rangle$-$\langle$x$\rangle$)/(N-1)

3. The attempt at a solution

c(0) = $\frac{1}{N}$$\sum$y(i)y(i)
= $\frac{1}{N}$$\sum$(x(i)2-2x(i)$\langle$x$\rangle$+$\langle$x$\rangle$2)
= $\langle$x2$\rangle$-2$\langle$x$\rangle$2+$\langle$x$\rangle$2
= $\langle$x2$\rangle$-$\langle$x$\rangle$2

Where did I mess up?

Last edited: Nov 27, 2011