mutual statistical independence

简明释义

相互统计独立

英英释义

例句

1.The two variables in the experiment were shown to have mutual statistical independence 相互统计独立, meaning changes in one did not affect the other.

实验中的两个变量被证明具有mutual statistical independence 相互统计独立，这意味着一个的变化不会影响另一个。

2.In a study on consumer behavior, the researchers found that the purchase of coffee and tea showed mutual statistical independence 相互统计独立, indicating that buying one does not influence the likelihood of buying the other.

在一项关于消费者行为的研究中，研究人员发现咖啡和茶的购买表现出mutual statistical independence 相互统计独立，这表明购买一个不会影响购买另一个的可能性。

3.The financial analyst determined that the stock prices of the two companies displayed mutual statistical independence 相互统计独立, suggesting that market movements of one do not impact the other.

金融分析师确定这两家公司的股票价格表现出mutual statistical independence 相互统计独立，这表明一个的市场波动不会影响另一个。

4.When analyzing the data, the team concluded that the events were mutual statistical independence 相互统计独立 because their joint probability was equal to the product of their individual probabilities.

在分析数据时，团队得出结论，这些事件是mutual statistical independence 相互统计独立，因为它们的联合概率等于各自概率的乘积。

5.In genetics, the traits of height and eye color can be considered mutual statistical independence 相互统计独立, as variations in one trait do not predict variations in the other.

在遗传学中，身高和眼睛颜色的特征可以被视为mutual statistical independence 相互统计独立，因为一个特征的变化并不预测另一个特征的变化。

作文

In the field of statistics and probability theory, the concept of mutual statistical independence plays a crucial role in understanding the relationships between different random variables. When two or more variables are said to be mutual statistical independence, it means that the occurrence of one variable does not affect the probability of occurrence of the other variable. This concept is fundamental in various applications, ranging from data analysis to machine learning, as it helps in simplifying complex models and making predictions more reliable.To illustrate this concept, consider two events A and B. If A and B are mutual statistical independence, the probability of both events occurring together can be calculated by multiplying their individual probabilities. Mathematically, this is represented as P(A and B) = P(A) * P(B). This property allows statisticians and data scientists to analyze large datasets more efficiently, as they can treat independent variables separately without worrying about their interdependencies.One practical application of mutual statistical independence can be found in the realm of genetics. In genetic studies, researchers often analyze the inheritance patterns of traits. If two traits are mutual statistical independence, the inheritance of one trait does not influence the inheritance of another. For instance, if we consider the traits of flower color and plant height in a certain species, if these traits are independent, knowing the color of a flower will not provide any information about the height of the plant. This allows geneticists to make predictions about the distribution of traits in a population based solely on their individual probabilities.Moreover, mutual statistical independence is also significant in the context of machine learning algorithms. Many algorithms, such as Naive Bayes classifiers, rely on the assumption that the features used for classification are independent of each other. This assumption simplifies the computation and enables the model to perform efficiently, even with a large number of features. However, it is essential to verify whether this assumption holds true in practice, as violating it can lead to inaccurate predictions.In conclusion, the concept of mutual statistical independence is vital in statistics and probability theory. It not only aids in simplifying complex relationships between random variables but also has practical applications in various fields such as genetics and machine learning. Understanding this concept allows researchers and practitioners to make more informed decisions and develop better predictive models. As we continue to gather more data in our increasingly data-driven world, the importance of recognizing and leveraging mutual statistical independence cannot be overstated. By doing so, we can enhance our analytical capabilities and improve our understanding of the intricate patterns that exist within our data.

在统计学和概率论的领域中，互相统计独立的概念在理解不同随机变量之间的关系中起着至关重要的作用。当两个或多个变量被称为互相统计独立时，这意味着一个变量的发生不会影响另一个变量的发生概率。这个概念在各种应用中都是基础，从数据分析到机器学习，因为它有助于简化复杂模型并使预测更可靠。为了说明这个概念，考虑两个事件A和B。如果A和B是互相统计独立的，则可以通过将它们各自的概率相乘来计算两个事件同时发生的概率。从数学上讲，这表示为P(A and B) = P(A) * P(B)。这个特性使得统计学家和数据科学家能够更有效地分析大型数据集，因为他们可以独立地处理独立变量，而不必担心它们之间的相互依赖性。互相统计独立的一个实际应用可以在遗传学领域找到。在遗传研究中，研究人员经常分析性状的遗传模式。如果两个性状是互相统计独立的，则一个性状的遗传不会影响另一个性状的遗传。例如，如果我们考虑某种植物的花色和植物高度这两个性状，如果这些性状是独立的，那么知道花的颜色并不会提供关于植物高度的任何信息。这使得遗传学家能够仅根据它们各自的概率对种群中性状的分布进行预测。此外，互相统计独立在机器学习算法的背景下也具有重要意义。许多算法，如朴素贝叶斯分类器，依赖于特征之间相互独立的假设。这个假设简化了计算，并使模型能够高效地执行，即使在特征数量庞大的情况下。然而，验证这一假设在实践中是否成立是至关重要的，因为违反这一假设可能导致不准确的预测。总之，互相统计独立的概念在统计学和概率论中至关重要。它不仅有助于简化随机变量之间复杂的关系，而且在遗传学和机器学习等各个领域都有实际应用。理解这一概念使研究人员和从业者能够做出更明智的决策并开发更好的预测模型。随着我们在日益数据驱动的世界中收集更多的数据，认识和利用互相统计独立的重要性不容小觑。通过这样做，我们可以增强我们的分析能力，改善我们对数据中存在的复杂模式的理解。