Law Of Large Numbers

Definition: Law Of Large Numbers

Law Of Large Numbers

Noun

1. (statistics) law stating that a large number of items taken at random from a population will (on the average) have the population statistics.

Specialty Definition: Law of large numbers

In probability theory, the weak law of large numbers states that if X₁, X₂, X₃, ... is an infinite sequence of random variables, all of which have the same expected value μ and the same finite variance σ², and they are uncorrelated (i.e., the correlation between any two of them is zero), then the sample average

converges in probability to μ. Somewhat less tersely: For any positive number ε, no matter how small, we have

Chebyshev's inequality is used to prove this result.

A consequence of the weak law of large numbers is the asymptotic equipartition property.

The strong law of large numbers states that if X₁, X₂, X₃, ... is an infinite sequence of random variables that are independent and identically distributed, and have a common expected value μ then

i.e., the sample average converges almost surely to μ.

This law justifies the intuitive interpretation of the expected value of a random variable as the "long-term average when sampling repeatedly".

Anagrams: Law Of Large Numbers

Scrabble® YAWL-Verified Anagrams
	Words within the letters "a-a-b-e-e-f-g-l-l-m-n-o-r-r-s-u-w"
	-5 letters: unreformable.
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Alternative Orthography: Law Of Large Numbers

Hexadecimal (or equivalents, 770AD-1900s) (references)

4C 61 77 4F 66 4C 61 72 67 65 4E 75 6D 62 65 72 73

Leonardo da Vinci (1452-1519; backwards) (references)

Binary Code (1918-1938, probably earlier) (references)

01001100 01100001 01110111 00100000 01001111 01100110 00100000 01001100 01100001 01110010 01100111 01100101 00100000 01001110 01110101 01101101 01100010 01100101 01110010 01110011

HTML Code (1990) (references)

&#76 &#97 &#119 &#32 &#79 &#102 &#32 &#76 &#97 &#114 &#103 &#101 &#32 &#78 &#117 &#109 &#98 &#101 &#114 &#115

ISO 10646 (1991-1993) (references)

004C 0061 0077 004F 0066 004C 0061 0072 0067 0065 004E 0075 006D 0062 0065 0072 0073

Encryption (beginner's substitution cypher): (references)

Law Of Large Numbers

Definition: Law Of Large Numbers