From Theorems 5 and 6, we can obtain easily the strong law of large numbers
for countable Markov chains indexed by a Cayley tree  and the strong law of large numbers
for finite Markov chains indexed by a uniformly bounded tree .
The last one is the Kolmogorov-type strong law of large numbers
for pairwise NQD random variables obtained by Chen , which plays an important role in proving the main results of the paper.
 Nagaev, S.V, On necessary and sufficient conditions for the strong law of large numbers
, Theory Prob.
However, the researchers found that people with high levels of interest in a topic rely more on the Law of Large Numbers
, assessing both consensus and the size of a poll.
In arguing for the law of large numbers
and broad historical forces, Wells is careful to add that he doesn't believe in the "Great Man" theory of history.
In Theorem 1.2 assuming that m = [infinity] and that the tail of distribution of [xi] is regularly varying at [infinity], a weak law of large numbers
They happen frequently, and independently of each other, so the law of large numbers
comes into play, and the insurer can reliably predict annual losses and set a premium that will cover them.
This is an illustration of the "law of large numbers
," which is the primary underpinning to the insurance mechanism.
Obviously it is in the best interest of all participants in the pool that their total number be as large as possible so the law of large numbers
will apply most effectively.
Life insurers have used mortality tables and "the law of large numbers
" to price policies for years.
Almost all of the things that classical science deals with involve zillions of items, and the Law of Large Numbers
guarantees that the form to the probability will be accurately expressed.
This contradicts the law of large numbers
which indicates that a large sample should be much more representative of the population (50% male) than a small sample.