expectation value

简明释义

期待值

英英释义

例句

1.In quantum mechanics, the expectation value 期望值 of an observable is calculated to predict the average outcome of measurements.

在量子力学中，某个可观测量的expectation value 期望值 被计算出来以预测测量的平均结果。

2.The expectation value 期望值 of a random variable can help in understanding its long-term behavior.

随机变量的expectation value 期望值 可以帮助理解其长期行为。

3.In statistics, the expectation value 期望值 is used to summarize the central tendency of a probability distribution.

在统计学中，expectation value 期望值 用于总结概率分布的集中趋势。

4.When analyzing stock prices, investors often look at the expectation value 期望值 to gauge potential returns.

在分析股票价格时，投资者通常会查看expectation value 期望值 以评估潜在回报。

5.The expectation value 期望值 of a game’s payoff can influence a player's decision-making process.

游戏收益的expectation value 期望值 可以影响玩家的决策过程。

作文

In the realm of mathematics and statistics, the concept of expectation value plays a crucial role in understanding random variables and their distributions. The expectation value is essentially the average or mean of a set of values, weighted by their probabilities. This concept allows researchers and analysts to summarize a large set of data into a single, representative number, providing insights into the overall behavior of the data. To illustrate this concept, consider a simple example of rolling a fair six-sided die. Each face of the die has an equal probability of landing face up, which is 1/6. To calculate the expectation value, we multiply each outcome by its probability: 1 (outcome) * (1/6) + 2 (outcome) * (1/6) + 3 (outcome) * (1/6) + 4 (outcome) * (1/6) + 5 (outcome) * (1/6) + 6 (outcome) * (1/6) = 21/6 = 3.5.Thus, the expectation value of rolling a six-sided die is 3.5. This means that if one were to roll the die a large number of times, the average result would approach 3.5, even though it is not possible to roll a 3.5 directly. This property of the expectation value demonstrates its utility in predictive modeling and decision-making processes.The expectation value is not limited to simple examples like dice rolls; it extends to more complex scenarios, such as financial markets, where investors use it to assess the expected returns of various investments. For instance, when evaluating a stock, an investor might consider the potential future prices of the stock and their associated probabilities. By calculating the expectation value of these prices, the investor can make informed decisions about whether to buy, hold, or sell the stock.Moreover, the expectation value serves as a foundation for various concepts in economics and game theory. In these fields, understanding the expectation value helps individuals and organizations strategize effectively by anticipating outcomes based on probabilistic models. For example, businesses often analyze the expectation value of different marketing strategies to determine which approach may yield the highest return on investment.In conclusion, the expectation value is a fundamental concept that aids in the analysis and interpretation of data across various disciplines. Its ability to condense complex information into a single representative figure makes it an invaluable tool for statisticians, economists, and decision-makers alike. By grasping the significance of the expectation value, one can enhance their analytical skills and improve their understanding of uncertainty and risk in both theoretical and practical contexts.

在数学和统计学领域，期望值的概念在理解随机变量及其分布中起着至关重要的作用。期望值本质上是一个数值集合的平均值或均值，按其概率加权。这个概念使研究人员和分析师能够将大量数据总结为一个单一的代表性数字，从而提供对数据整体行为的洞察。为了说明这个概念，考虑一个简单的例子：掷一个公平的六面骰子。骰子的每个面都有相等的概率朝上，即1/6。要计算期望值，我们将每个结果乘以其概率：1（结果）*(1/6) + 2（结果）*(1/6) + 3（结果）*(1/6) + 4（结果）*(1/6) + 5（结果）*(1/6) + 6（结果）*(1/6) = 21/6 = 3.5。因此，掷一个六面骰子的期望值是3.5。这意味着，如果人们掷骰子的次数足够多，平均结果将接近3.5，尽管不可能直接掷出3.5。这个期望值的特性展示了它在预测建模和决策过程中的实用性。期望值不仅限于像掷骰子这样的简单示例；它扩展到更复杂的场景，例如金融市场，投资者利用它评估各种投资的预期回报。例如，在评估股票时，投资者可能会考虑该股票未来价格的潜在值及其相关概率。通过计算这些价格的期望值，投资者可以就是否购买、持有或出售股票做出明智的决定。此外，期望值作为经济学和博弈论中各种概念的基础。在这些领域，理解期望值有助于个人和组织通过基于概率模型的预期结果进行有效的战略规划。例如，企业通常分析不同营销策略的期望值，以确定哪种方法可能带来最高的投资回报。总之，期望值是一个基本概念，有助于在各个学科中进行数据分析和解释。它将复杂信息浓缩为一个单一的代表性数字的能力，使其成为统计学家、经济学家和决策者不可或缺的工具。通过掌握期望值的重要性，人们可以增强分析能力，提高对理论和实际背景中不确定性和风险的理解。