Talk:Proof of the law of large numbers

Someone, perhaps me, should write one of the proof of the strong law. Aastrup 13:09, 25 July 2007 (UTC)


 * The proof that uses characteristic functions seems incomplete to me. From the provided proof it only follows that the limit of the characteristic functions converges to the exponential near the origin, but not necessarily elsewhere. Unfortunately, I am unable to fix this myself. 193.85.150.3 18:22, 17 September 2007 (UTC)


 * are you referring to :$$\varphi_{\overline{X}_n}(t)= \left[\varphi_X\left({t \over n}\right)\right]^n = \left[1 + i\mu{t \over n} + o\left({t \over n}\right)\right]^n \, \rightarrow \, e^{it\mu}, \quad \textrm{as} \quad n \rightarrow \infty.$$? Move n to infinity while fixing t. In that way the convergence is proved for all t. --Novwik 08:36, 9 October 2007 (UTC)

Incorrect use of subpages
The title has to be changed: subpages are no longer used in the wikipedia mainspace: WP:SP. 128.139.226.37 (talk) 11:24, 21 February 2008 (UTC)

Note that the (Chebyshev's) weak law of large numbers is more general than the one proven here; in particular, there is no need for the iid assumption (only finite but potentially different means, finite but potentially different variances and their average must be also finite, and the linear independence of random variables). I think this must be stated explicitely in the article or, better, more general proof shall be given VZ7 (talk) 16:54, 19 January 2010 (UTC)