Ad
related to: law of large numbers proof
Search results
Results From The WOW.Com Content Network
They are called the strong law of large numbers and the weak law of large numbers. [ 16 ] [ 1 ] Stated for the case where X 1 , X 2 , ... is an infinite sequence of independent and identically distributed (i.i.d.) Lebesgue integrable random variables with expected value E( X 1 ) = E( X 2 ) = ... = μ , both versions of the law state that the ...
The law of truly large numbers (a statistical adage), attributed to Persi Diaconis and Frederick Mosteller, states that with a large enough number of independent samples, any highly implausible (i.e. unlikely in any single sample, but with constant probability strictly greater than 0 in any sample) result is likely to be observed. [1]
2 Proof. 3 References. Toggle the table of contents. ... It follows from Kolmogorov's inequality and is used in one proof of the strong law of large numbers.
Kolmogorov's three-series theorem, combined with Kronecker's lemma, can be used to give a relatively easy proof of the Strong Law of Large Numbers. [ 1 ] Statement of the theorem
The lemma is often used in the proofs of theorems concerning sums of independent random variables such as the strong Law of large numbers. The lemma is named after the German mathematician Leopold Kronecker.
This result is known as the weak law of large numbers. ... The proof can be found in Page 126 (Theorem 5.3.4) of the book by Kai Lai Chung. [13]
For premium support please call: 800-290-4726 more ways to reach us
The law of iterated logarithms operates "in between" the law of large numbers and the central limit theorem.There are two versions of the law of large numbers — the weak and the strong — and they both state that the sums S n, scaled by n −1, converge to zero, respectively in probability and almost surely: