Noun Phrase
/sɪˈmɛtrɪk ˈrændəm ˈværiəblz/
Meaning: Symmetric random variables are a pair of random variables whose distributions are identical when reflected about a central point (often the mean). In more technical terms, a random variable (X) is said to be symmetric if for any value (a), the probability of (X) being less than (a) is the same as the probability of (X) being greater than (2\mu - a) (where (\mu) is the mean of (X)).
Frequency of Use: The phrase "symmetric random variables" is more commonly used in academic and statistical contexts, particularly in probability theory and statistics, than in everyday oral speech. Its use is prevalent in research papers, textbooks, and lectures focused on statistics and probability.
Symmetric random variables are important in the study of statistical properties.
(Симметричные случайные величины важны в изучении статистических свойств.)
In many cases, symmetric random variables can simplify the mathematical analysis.
(Во многих случаях симметричные случайные величины могут упростить математический анализ.)
Researchers often use symmetric random variables when modeling data distributions.
(Исследователи часто используют симметричные случайные величины при моделировании распределений данных.)
The term "symmetric random variables" is not widely featured in idiomatic expressions, as it belongs to a specialized lexicon. However, within the context of statistics and probability, we can consider terms related to symmetry and variables in statistical discussions, leading to relevant phrases.
"Mirror symmetry" in statistics emphasizes the balance of data points around the mean.
(Зеркальная симметрия в статистике подчеркивает баланс наблюдений вокруг среднего.)
"Symmetric distributions" can often lead to easier predictions in modeling.
(Симметричные распределения могут привести к более простым предсказаниям в моделировании.)
"In terms of symmetry," we can analyze both sides of the distribution equally.
(В терминах симметрии, мы можем равномерно анализировать обе стороны распределения.)
"Achieving balance" in data sets often requires the use of symmetric variables.
(Достижение баланса в наборах данных часто требует использования симметричных переменных.)
The word "symmetric" derives from the Greek word "symmetricus," which means "having the same measure." The concept of symmetry has been a fundamental idea in mathematics and science. The term "random variable" combines "random," which comes from Old French or Latin sources meaning "by chance," and "variable," from the Latin "variabilis," meaning "changeable" or "able to vary." Together, they denote a variable whose value is subject to randomness.
Synonyms: - Balanced random variables - Identically distributed variables
Antonyms: - Asymmetric random variables - Skewed random variables
This comprehensive overview encapsulates the term "symmetric random variables," offering insights into its usage, example sentences, idiomatic expressions, historical background, and related terms.