Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Strong Law of Large Numbers

  1. Jun 27, 2005 #1
    For the Strong Law of Large Numbers, as far as I know it applies when, let say, the random variables {Xn: n=1,2,...} are iid, hence uncorrelated, their second moments have a common bound and they have a finite mean mu.
    What else I must consider? Is there anyother consideretion or case when the SLLN does not apply?
  2. jcsd
  3. Jun 28, 2005 #2


    User Avatar
    Science Advisor

    There are weaker conditions for the strong law to hold.

    For example, the Kolmogoroff Criterion does not require the distributions be identical.
    It needs sum (Vk/k2) be a convergent series (V=variance).

    Alternatively if the distributions are identical, all you need is the mean - the variance may be infinite.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook