expectation value

简明释义

期望值

英英释义

例句

1.To find the expectation value 期望值 of a die roll, you average the outcomes weighted by their probabilities.

要找到掷骰子的expectation value 期望值，你需要根据各个结果的概率加权计算平均值。

2.The expectation value 期望值 in statistics is crucial for understanding the central tendency of a dataset.

统计学中的expectation value 期望值对于理解数据集的集中趋势至关重要。

3.The expectation value 期望值 of a random variable can be calculated using its probability distribution.

随机变量的expectation value 期望值可以通过其概率分布来计算。

4.In quantum mechanics, the expectation value 期望值 of an observable gives us the average result we would expect from many measurements.

在量子力学中，一个可观察量的expectation value 期望值提供了我们从许多测量中期望得到的平均结果。

5.In finance, the expectation value 期望值 of an investment's return helps investors make informed decisions.

在金融中，投资回报的expectation value 期望值帮助投资者做出明智的决策。

作文

In the realm of statistics and probability, the concept of expectation value plays a crucial role in understanding the average outcome of random variables. The expectation value is essentially a measure of the center of a probability distribution, providing a single number that summarizes the entire distribution's behavior. To grasp this concept better, let’s delve into its definition, significance, and applications in various fields.The expectation value, often denoted as E(X) for a random variable X, is calculated by taking the sum of all possible values of X, each multiplied by its respective probability of occurrence. Mathematically, it is expressed as:E(X) = Σ [x * P(x)]where x represents the possible outcomes and P(x) denotes the probability of each outcome. This formula illustrates that the expectation value is a weighted average, where outcomes with higher probabilities have a more significant influence on the final result.Understanding the expectation value is essential because it provides insights into what one can expect on average from a random process. For instance, in gambling, knowing the expectation value of a game can help players make informed decisions about whether to participate. If the expectation value is negative, it indicates that, on average, players will lose money over time, while a positive expectation value suggests potential gains.Moreover, the expectation value extends beyond games of chance; it is widely used in economics, finance, and insurance. In finance, investors often look at the expectation value of returns on investments to assess their risk and potential profit. For example, if an investor is considering two stocks, they may calculate the expectation value of each stock's return based on historical data and market trends. This analysis aids in making strategic investment choices.In addition to its applications in finance, the expectation value is also pivotal in scientific research and experiments. Researchers utilize the expectation value to predict outcomes based on varying conditions. For instance, in a physics experiment measuring particle collisions, scientists might calculate the expectation value of certain measurable quantities to understand the underlying phenomena better. This predictive power is invaluable for advancing knowledge and technology.Furthermore, the expectation value can aid in decision-making processes under uncertainty. Businesses often employ statistical models that incorporate the expectation value to evaluate different scenarios and their potential impacts. By analyzing the expectation value of various strategies, companies can optimize their operations and enhance profitability.In conclusion, the expectation value is a fundamental concept in probability and statistics that encapsulates the average outcome of random variables. Its ability to summarize complex distributions into a single numerical value makes it indispensable across various domains, including gambling, finance, scientific research, and business decision-making. By understanding and applying the expectation value, individuals and organizations can make more informed choices and navigate uncertainties effectively. As we continue to encounter randomness in our lives, the expectation value remains a powerful tool for predicting and understanding the world around us.

在统计学和概率论的领域中，期望值的概念在理解随机变量的平均结果方面发挥着至关重要的作用。期望值本质上是概率分布中心的度量，提供了一个单一的数字来总结整个分布的行为。为了更好地掌握这一概念，让我们深入探讨其定义、重要性以及在各个领域的应用。期望值通常用E(X)表示，其中X为随机变量，通过将X的所有可能值相加，每个值乘以其发生的概率来计算。数学上，它的表达式为：E(X) = Σ [x * P(x)]其中x代表可能的结果，P(x)表示每个结果的概率。这个公式表明，期望值是一个加权平均值，概率较高的结果对最终结果有更大的影响。理解期望值至关重要，因为它提供了关于从随机过程预期的平均结果的见解。例如，在赌博中，了解游戏的期望值可以帮助玩家做出是否参与的明智决策。如果期望值为负，则表明玩家在时间上会平均损失金钱，而正的期望值则暗示潜在收益。此外，期望值不仅限于机会游戏；它在经济学、金融和保险等领域被广泛使用。在金融领域，投资者通常关注投资回报的期望值来评估风险和潜在利润。例如，如果一位投资者正在考虑两只股票，他们可能会根据历史数据和市场趋势计算每只股票回报的期望值。这种分析有助于制定战略投资选择。除了在金融中的应用外，期望值在科学研究和实验中也至关重要。研究人员利用期望值根据不同条件预测结果。例如，在测量粒子碰撞的物理实验中，科学家可能会计算某些可测量量的期望值，以更好地理解基础现象。这种预测能力对推动知识和技术的进步至关重要。此外，期望值可以帮助在不确定性下的决策过程。企业通常采用包含期望值的统计模型来评估不同情境及其潜在影响。通过分析各种策略的期望值，公司可以优化运营并提高盈利能力。总之，期望值是概率和统计学中的一个基本概念，概括了随机变量的平均结果。它能够将复杂的分布总结为一个单一的数值，使其在赌博、金融、科学研究和商业决策等多个领域不可或缺。通过理解和应用期望值，个人和组织可以做出更明智的选择，有效应对不确定性。随着我们继续在生活中遇到随机性，期望值仍然是预测和理解周围世界的强大工具。