The technique used to study the strong

law of large numbers for countable Markov chains indexed by trees is different from that for finite case.

Under the conditions of Theorem 3 and [a.sub.2n] [less than or equal to] C[a.sub.n], we can get the Marcinkiewicz-Zygmund-type strong

law of large numbers for pairwise NQD random variables as follows:

Theorem .3.1 : The strong

law of large numbers for the sequence of random variables

(22), we recover the

law of large numbers. Taking the limit N [right arrow] m in eqn.

The

Law of Large Numbers can be traced back to Jakob Bernoulli's 1713 work "The Art of Conjecturing." The theorem roughly states that the larger a random sample is the more its mean will mirror that of the total population.

"OK, we have to remember the

law of large numbers though.

The

law of large numbers tells us that when dealing with a large number of random values, overall leading parameters such as average, median, and standard deviation of the values can be expected to remain constant from one day to the next.

the

law of large numbers; comparative citizenship in Europe; natality policies in multicultural societies; state support for demographic transformation; immigration policy and restrictions; and, manipulating demographics, among others.

*

LAW OF LARGE NUMBERS. Forecasting the future can make use of statistical probability.

We also establish a weak

law of large numbers for [V.sub.n] under a regular variation assumption.

residents age 18 or older) and, thanks to the

law of large numbers, you can estimate what the entire group might do (say, 2008 presidential vote preference) with known levels of accuracy and risk (with a 600 sample, 95 percent certain that the estimate is within plus-or-minus 4 percent).

"Due to the

law of large numbers, traditional IT product models are becoming victims of their own success, while the relative smallness of new approaches facilitates growth much more easily," said Pring.