expected value

简明释义

期望值

英英释义

例句

1.In decision-making, calculating the expected value 期望值 can help choose the best option.

在决策中，计算期望值 expected value 可以帮助选择最佳选项。

2.The expected value 期望值 of a game can indicate whether it is fair or biased.

一个游戏的期望值 expected value 可以指示它是公平的还是有偏见的。

3.The expected value 期望值 of a lottery ticket is usually much lower than the cost of the ticket.

彩票的期望值 expected value 通常远低于彩票的成本。

4.In gambling, the expected value 期望值 of a bet helps players determine if it's worth placing.

在赌博中，期望值 expected value 可以帮助玩家判断是否值得下注。

5.Investors often calculate the expected value 期望值 of their portfolios to assess potential returns.

投资者通常会计算他们投资组合的期望值 expected value 来评估潜在回报。

作文

In the realm of probability and statistics, the concept of expected value plays a crucial role in decision-making processes. The expected value is essentially a weighted average of all possible outcomes of a random variable, where each outcome is multiplied by the probability of its occurrence. This mathematical expectation provides a single number that summarizes the central tendency of a probability distribution, allowing individuals and organizations to make informed choices based on potential risks and rewards.To illustrate the importance of expected value, consider a simple example involving a game of dice. Imagine you are playing a game where you roll a fair six-sided die. If you roll a 1, you lose $1; if you roll a 2, you win $2; if you roll a 3, you win $3; if you roll a 4, you win $4; if you roll a 5, you win $5; and if you roll a 6, you win $6. To find the expected value of this game, you would calculate the outcomes as follows:- The probability of rolling any specific number on the die is 1/6.- Therefore, the expected value can be computed as: Expected Value = (1/6)(-1) + (1/6)(2) + (1/6)(3) + (1/6)(4) + (1/6)(5) + (1/6)(6)This simplifies to: Expected Value = (-1 + 2 + 3 + 4 + 5 + 6) / 6 = 19/6 ≈ 3.17From this calculation, we see that the expected value of playing the game is approximately $3.17. This means that, on average, if you were to play this game many times, you could expect to win about $3.17 per game. Thus, the expected value serves as a useful indicator of whether or not a game or investment is worth pursuing.In the context of business and finance, the expected value can guide companies in making strategic decisions. For instance, when evaluating a new project, a company might assess various scenarios—such as best-case, worst-case, and most likely outcomes—and assign probabilities to each scenario. By calculating the expected value of the project's potential returns, the company can determine whether the project is likely to yield a positive return on investment.Moreover, the expected value is also a fundamental concept in gambling and insurance. Gamblers often analyze the expected value of different bets to identify which ones offer the best chances of winning. Similarly, insurance companies use expected value calculations to set premiums and manage risk effectively. By understanding the expected value of various claims, insurers can ensure they remain profitable while providing coverage to their clients.In conclusion, the concept of expected value is an essential tool in both theoretical and practical applications across various fields. It helps individuals and organizations make rational decisions based on potential outcomes and associated probabilities. By grasping the significance of expected value, one can navigate uncertainty with greater confidence and clarity, ultimately leading to more informed choices in life, business, and beyond.

在概率和统计的领域中，期望值的概念在决策过程中发挥着至关重要的作用。期望值本质上是随机变量所有可能结果的加权平均，每个结果都乘以其发生的概率。这个数学期望提供了一个单一的数字，总结了概率分布的集中趋势，使个人和组织能够根据潜在的风险和回报做出明智的选择。为了说明期望值的重要性，考虑一个简单的骰子游戏的例子。假设你正在玩一个游戏，你要掷一个公平的六面骰子。如果你掷出1，你将损失1美元；如果你掷出2，你将赢得2美元；如果你掷出3，你将赢得3美元；如果你掷出4，你将赢得4美元；如果你掷出5，你将赢得5美元；如果你掷出6，你将赢得6美元。要找出这个游戏的期望值，你需要按如下方式计算结果：- 掷出骰子上任何特定数字的概率为1/6。- 因此，期望值可以计算为： 期望值 = (1/6)(-1) + (1/6)(2) + (1/6)(3) + (1/6)(4) + (1/6)(5) + (1/6)(6)这简化为： 期望值 = (-1 + 2 + 3 + 4 + 5 + 6) / 6 = 19/6 ≈ 3.17从这个计算中，我们看到，这个游戏的期望值大约是3.17美元。这意味着，如果你多次玩这个游戏，平均而言，你可以期待每场游戏赢得大约3.17美元。因此，期望值作为一个有用的指标，可以帮助我们判断一个游戏或投资是否值得追求。在商业和金融的背景下，期望值可以指导公司做出战略决策。例如，在评估一个新项目时，公司可能会评估各种情景——如最佳情况、最坏情况和最可能情况，并给每种情景分配概率。通过计算项目潜在回报的期望值，公司可以判断该项目是否可能带来正的投资回报。此外，期望值也是赌博和保险中的基本概念。赌徒通常会分析不同投注的期望值，以确定哪些投注提供最佳的获胜机会。同样，保险公司利用期望值计算来设定保费并有效管理风险。通过理解各种索赔的期望值，保险公司可以确保在为客户提供保障的同时保持盈利。总之，期望值的概念是理论和实践应用中各个领域的重要工具。它帮助个人和组织根据潜在结果和相关概率做出理性决策。通过掌握期望值的重要性，人们可以更有信心和清晰地应对不确定性，最终在生活、商业等方面做出更明智的选择。