Find out information about Poisson's Law of Large Numbers. The law that if, in a collection of independent identical experiments, N represents the number of occurrences of an event B in n trials.
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.In, the law of large numbers ( LLN) is a that describes the result of performing the same experiment a large number of times. According to the law, the of the results obtained from a large number of trials should be close to the, and will tend to become closer as more trials are performed.The LLN is important because it guarantees stable long-term results for the averages of some random events. For example, while a casino may lose money in a single spin of the wheel, its earnings will tend towards a predictable percentage over a large number of spins. Any winning streak by a player will eventually be overcome by the parameters of the game. It is important to remember that the law only applies (as the name indicates) when a large number of observations is considered.
There is no principle that a small number of observations will coincide with the expected value or that a streak of one value will immediately be 'balanced' by the others (see the ). 1)(Lebesgue integrability of X j means that the expected value E( X j) exists according to and is finite. It does not mean that the associated probability measure is with respect to.)An assumption of finite Var( X 1) = Var( X 2) =.