1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Proof that's missing a step

  1. Nov 27, 2011 #1
    1. The problem statement, all variables and given/known data

    Show that

    c(0) = [itex]\sigma[/itex][itex]^{2}[/itex]

    2. Relevant equations

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

    y(i) = x(i)-[itex]\langle[/itex]x[itex]\rangle[/itex]

    [itex]\langle[/itex]x[itex]\rangle[/itex]=[itex]\frac{1}{N}[/itex][itex]\sum[/itex]x(i)

    [itex]\langle[/itex]x2[itex]\rangle[/itex]=[itex]\frac{1}{N}[/itex][itex]\sum[/itex]x(i)2

    Edit: the other summations go from 1 to N

    Edit: forgot sigma

    [itex]\sigma[/itex]2 = ([itex]\langle[/itex]x2[itex]\rangle[/itex]-[itex]\langle[/itex]x[itex]\rangle[/itex])/(N-1)

    3. The attempt at a solution

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



    Where did I mess up?
     
    Last edited: Nov 27, 2011
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Similar Discussions: Proof that's missing a step
  1. Missing gap in proof (Replies: 1)

  2. A Step Function Proof (Replies: 4)

Loading...