From Theorems 5 and 6, we can obtain easily the strong

law of large numbers for countable Markov chains indexed by a Cayley tree [16] and the strong

law of large numbers for finite Markov chains indexed by a uniformly bounded tree [15].

The last one is the Kolmogorov-type strong

law of large numbers for pairwise NQD random variables obtained by Chen [23], which plays an important role in proving the main results of the paper.

[2] 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 is established.

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.