mathematical expection

简明释义

数学期望

英英释义

例句

1.The mathematical expectation 数学期望 can be calculated by multiplying each possible outcome by its probability and summing these products.

可以通过将每个可能结果乘以其概率并求和来计算数学期望 数学期望。

2.In finance, investors use mathematical expectation 数学期望 to evaluate the potential returns of different investment options.

在金融领域，投资者使用数学期望 数学期望 来评估不同投资选项的潜在回报。

3.The mathematical expectation 数学期望 of a fair die roll is 3.5, as it represents the average of all possible outcomes.

公平骰子的数学期望 数学期望 是3.5，因为它代表所有可能结果的平均值。

4.When analyzing games of chance, the mathematical expectation 数学期望 helps players understand their average expected winnings.

在分析机会游戏时，数学期望 数学期望 帮助玩家理解他们的平均预期收益。

5.In statistics, the mathematical expectation 数学期望 of a random variable provides a measure of the center of its distribution.

在统计学中，随机变量的数学期望 数学期望 提供了其分布中心的度量。

作文

In the realm of statistics and probability, one of the most fundamental concepts is the mathematical expectation. This term refers to the average or mean value that one can anticipate from a random variable based on its probability distribution. Essentially, it provides a measure of the center of the distribution of a random variable, allowing us to make informed decisions based on expected outcomes. Understanding mathematical expectation is crucial for anyone involved in fields such as finance, insurance, economics, and various branches of science.To illustrate the concept of mathematical expectation, consider a simple example involving a fair six-sided die. When you roll the die, there are six possible outcomes: 1, 2, 3, 4, 5, and 6. Each number has an equal probability of occurring, which is 1/6. To calculate the mathematical expectation, we multiply each outcome by its probability and then sum these products:(1 * 1/6) + (2 * 1/6) + (3 * 1/6) + (4 * 1/6) + (5 * 1/6) + (6 * 1/6) = 21/6 = 3.5.Thus, the mathematical expectation of rolling a fair die is 3.5. This means that if one were to roll the die a large number of times, the average result would converge to 3.5 over time.The importance of mathematical expectation extends beyond simple games of chance. In finance, for instance, investors use this concept to evaluate the potential returns of different investment options. By calculating the mathematical expectation of various scenarios, they can assess the risk and reward associated with each investment. For example, if an investor considers two stocks, one with a high potential return but also high risk, and another with a lower return but more stability, the mathematical expectation helps them determine which stock aligns better with their financial goals and risk tolerance.Moreover, mathematical expectation plays a significant role in insurance. Insurance companies rely on this concept to set premiums and manage risk. By analyzing historical data, they can estimate the mathematical expectation of claims for a particular group of policyholders. This allows them to determine how much to charge for coverage while ensuring they remain profitable.In conclusion, the concept of mathematical expectation is not only a theoretical construct but a practical tool that influences decision-making across various domains. Whether in gaming, investing, or risk management, understanding the mathematical expectation enables individuals and organizations to navigate uncertainty with greater confidence. As we continue to analyze data and make predictions about future events, the significance of mathematical expectation will undoubtedly remain a cornerstone of statistical reasoning and analysis.

在统计学和概率论的领域中，最基本的概念之一是数学期望。这个术语指的是根据随机变量的概率分布可以预期的平均值或均值。基本上，它提供了一个随机变量分布中心的度量，使我们能够根据预期结果做出明智的决策。理解数学期望对于任何参与金融、保险、经济学和各种科学分支的人来说都是至关重要的。为了说明数学期望的概念，考虑一个简单的例子，涉及一个公平的六面骰子。当你掷骰子时，有六个可能的结果：1、2、3、4、5和6。每个数字发生的概率相等，即1/6。要计算数学期望，我们将每个结果乘以其概率，然后求和：(1 * 1/6) + (2 * 1/6) + (3 * 1/6) + (4 * 1/6) + (5 * 1/6) + (6 * 1/6) = 21/6 = 3.5。因此，掷一个公平骰子的数学期望是3.5。这意味着，如果一个人掷骰子很多次，结果的平均值将随着时间的推移趋近于3.5。数学期望的重要性超出了简单的机会游戏。在金融领域，例如，投资者使用这个概念来评估不同投资选项的潜在回报。通过计算各种情景的数学期望，他们可以评估与每项投资相关的风险和回报。例如，如果一位投资者考虑两只股票，一只具有高潜在回报但风险也高，另一只具有较低回报但更稳定，数学期望帮助他们确定哪只股票更符合他们的财务目标和风险承受能力。此外，数学期望在保险中也起着重要作用。保险公司依赖这一概念来设定保费和管理风险。通过分析历史数据，他们可以估计特定保单持有者群体的索赔数学期望。这使他们能够确定收取多少费用以获得保障，同时确保盈利。总之，数学期望的概念不仅是一个理论构造，而是一个实用工具，影响着各个领域的决策。在游戏、投资或风险管理中，理解数学期望使个人和组织能够更自信地应对不确定性。随着我们继续分析数据并对未来事件进行预测，数学期望的重要性无疑将继续成为统计推理和分析的基石。