law of large numbers

简明释义

大数定律

英英释义

例句

1.The casino relies on the law of large numbers to ensure that they make a profit over time.

赌场依靠大数法则来确保他们随着时间的推移获利。

2.The law of large numbers suggests that as more trials are conducted, the average of the results will converge on the expected value.

大数法则表明，随着试验次数的增加，结果的平均值将趋近于期望值。

3.Investors believe in the law of large numbers when they diversify their portfolios to reduce risk.

投资者在分散投资组合以降低风险时相信大数法则。

4.In insurance, companies use the law of large numbers to predict claims based on a large pool of policyholders.

在保险行业，公司利用大数法则根据大量投保人预测索赔。

5.A sample size of 30 is often considered sufficient for the law of large numbers to hold true in statistics.

在统计学中，样本量为30通常被认为足以使大数法则成立。

作文

The concept known as the law of large numbers is a fundamental principle in probability and statistics that describes how the average of a large number of trials will converge to the expected value. This principle is crucial for understanding how randomness works in various fields, such as finance, insurance, and even everyday decision-making. Essentially, the law of large numbers states that as the number of trials increases, the sample mean will get closer to the population mean. To illustrate this concept, consider a simple example involving a fair six-sided die. If you roll the die just a few times, you might get a series of results that are quite varied; perhaps you roll a 2, then a 5, and then a 1. The average of these rolls can be significantly different from the expected average of 3.5 (the mean of all possible outcomes). However, if you were to roll the die a thousand times, the average of those rolls would likely be much closer to 3.5. This phenomenon occurs because the extremes tend to cancel each other out over a larger number of trials, leading to a more stable and reliable average. The law of large numbers has significant implications in many real-world scenarios. For instance, in finance, investors often rely on this principle when assessing the risk and return of their portfolios. They know that while individual stock prices may fluctuate wildly, over time, the average return of a diversified portfolio will stabilize and reflect the overall market trend. This understanding helps investors make informed decisions about where to allocate their resources. In the field of insurance, companies use the law of large numbers to predict future claims. By analyzing data from a large pool of policyholders, insurers can estimate how many claims they will receive and set premiums accordingly. This allows them to manage risk effectively and ensure that they remain profitable while providing coverage to their clients. Moreover, the law of large numbers is not limited to financial applications. It also plays a role in scientific research and experimentation. For example, when conducting clinical trials for new medications, researchers must gather data from a sufficiently large group of participants to ensure that the results are statistically significant. If the sample size is too small, the findings may be skewed by outliers or random chance, leading to inaccurate conclusions. In conclusion, the law of large numbers is a powerful concept that underscores the importance of sample size in statistical analysis and decision-making. It provides a framework for understanding how averages behave in the face of randomness and variability. By recognizing the significance of this law, individuals and organizations can better navigate uncertainty and make more informed choices based on empirical evidence. Whether in finance, insurance, or scientific research, the law of large numbers remains a cornerstone of effective analysis and prediction, highlighting the reliability that emerges from larger datasets. Therefore, it is essential for students, professionals, and anyone interested in data-driven decision-making to grasp the implications of the law of large numbers and apply it appropriately in their respective fields.

被称为大数法则的概念是概率和统计学中的一个基本原则，描述了大量试验的平均值将如何收敛到期望值。这个原则对于理解随机性在金融、保险甚至日常决策等各个领域的运作至关重要。基本上，大数法则表明，随着试验次数的增加，样本均值将越来越接近总体均值。为了说明这一概念，考虑一个简单的例子，涉及一个公平的六面骰子。如果你只掷骰子几次，你可能会得到一系列相当不同的结果；也许你先掷出2，然后是5，再然后是1。这些掷骰子的平均值可能与所有可能结果的期望平均值3.5（所有可能结果的均值）有显著差异。然而，如果你掷骰子一千次，这些掷出的平均值可能会更接近3.5。这一现象发生的原因是，随着试验次数的增多，极端值往往会相互抵消，从而导致更稳定、更可靠的平均值。大数法则在许多现实场景中具有重要意义。例如，在金融领域，投资者在评估投资组合的风险和回报时通常依赖于这一原则。他们知道，虽然单个股票价格可能剧烈波动，但随着时间的推移，分散投资组合的平均回报将稳定下来，并反映整体市场趋势。这种理解帮助投资者就资源的配置做出明智的决策。在保险领域，公司利用大数法则来预测未来的索赔。通过分析来自大量投保人的数据，保险公司可以估算他们将收到多少索赔，并相应地设定保费。这使他们能够有效管理风险，并确保在为客户提供保障的同时保持盈利。此外，大数法则并不仅限于金融应用。它在科学研究和实验中也发挥着作用。例如，在进行新药的临床试验时，研究人员必须从足够大的参与者群体中收集数据，以确保结果具有统计显著性。如果样本量太小，结果可能会受到异常值或随机机会的影响，导致不准确的结论。总之，大数法则是一个强大的概念，强调了样本大小在统计分析和决策中的重要性。它为理解平均值在随机性和变异性面前的行为提供了框架。通过认识到这一法则的重要性，个人和组织可以更好地应对不确定性，并根据实证证据做出更明智的选择。无论是在金融、保险还是科学研究中，大数法则仍然是有效分析和预测的基石，突显出大型数据集所产生的可靠性。因此，学生、专业人士以及任何对数据驱动决策感兴趣的人都应掌握大数法则的含义，并在各自领域中适当地应用。