Kolmogorov's strong law of large numbers

9.9

A theorem that says the average of many independent random results almost certainly equals the true average

noun

Specialized

: ley fuerte de los grandes números de Kolmogorov

According to Kolmogorov's strong law of large numbers, sample averages converge to the expected value.

Examples

Many statistical simulations rely on Kolmogorov's strong law of large numbers to ensure accuracy as the number of trials increases.
The professor explained Kolmogorov's strong law of large numbers during the advanced probability lecture.
According to Kolmogorov's strong law of large numbers, the sample mean will almost surely converge to the expected value.
Have you studied Kolmogorov's strong law of large numbers in your probability class?
According to Kolmogorov's strong law of large numbers, the sample mean will almost surely converge to the expected value.
Many statistical simulations rely on Kolmogorov's strong law of large numbers to ensure accuracy as the number of trials increases.
The professor explained Kolmogorov's strong law of large numbers during the advanced probability lecture.

Synonyms

strong law of large numbers

vsKolmogorov's strong law of large numbers

Specialized

9.1

The average of many separate random results becomes almost always close to the true average

allows independent variables that need not be identically distributed under broader conditions

Surface Forms

Kolmogorov's strong law of large numbers singular

Kolmogorov's strong laws of large numbers plural

Morphology

Kolmogorov's + strong + law + of + large + number

Although the individual words signal that this is a mathematical "law" concerning "large numbers" and that it is a "strong" (i.e. stronger) variant, the specific technical meaning (almost-sure convergence of sample averages under certain conditions) is specialized and not derivable from the constituents by a B1 learner. The presence of a proper name (Kolmogorov's) and the technical nature of the phrase make the overall meaning only partially predictable, so learners may grasp the general idea but not the precise statistical content.

Etymology

Kolmogorov's strong law of large numbers is named after the mathematician Andrey Kolmogorov, who showed that if you repeat a random action many times the average result becomes steady. Think of tossing a coin again and again: the average number of heads will 'settle down' to the 'expected value', so the idea means that averages move towards the true value as the number of tries grows.