If the Strong Law of Large Numbers imply the Weak Law, why do we have a Weak Law of Large Numbers?
2026-03-27 04:17:42.1774585062
Strong Law of Large Numbers imply Weak Law
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A weak law may come with some estimate of the rate of convergence which is not available for the strong law. In practical situations, such as statistics, you never have a whole infinite sequence of trials, only a finite sequence. Yet you would still like to deduce something about the underlying probability distribution.
The textbook
Chung, Kai Lai, Elementary probability theory with stochastic processes, Undergraduate Texts in Mathematics. New York - Heidelberg - Berlin: Springer-Verlag. X, 325 p. Cloth DM 29.40; $ 12.00 (1974). ZBL0293.60001.
perplexes students by showing two quotes on the same page, one saying that the strong law is superior to the weak, and the other saying the weak law is superior to the strong. This leaves the poor instructor (me) to explain the discrepancy!
Here it is, from page 233 in the first edition: