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Jan 10, 2019 at 14:23 history edited Denis Serre CC BY-SA 4.0
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Mar 21, 2013 at 5:03 comment added Russ Woodroofe For the SLLN, isn't there an issue in exchanging the limit with the integral implicit in the variance? Even for the WLLN, it seems to me that the technical details needed (e.g. Chebyshev's Inequality) rather "ruin the pristine elegance", to quote a previous comment.
Mar 20, 2013 at 22:54 comment added Nate Eldredge It does constitute a proof of the weak law of large numbers, and it shows that if the limit $\lim_{n \to \infty} \frac{1}{n} \sum_{i=1}^n X_i$ exists almost surely, it must equal $\mu$.
Mar 19, 2013 at 19:38 history answered Russ Woodroofe CC BY-SA 3.0