expected value

简明释义

预期值

英英释义

例句

1.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。

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

投资者通常计算他们投资组合的期望值 expected value 来评估潜在收益。

3.To make informed decisions, businesses analyze the expected value 期望值 of different marketing strategies.

为了做出明智的决策，企业分析不同营销策略的期望值 expected value。

4.The expected value 期望值 of a lottery ticket is typically much lower than its cost.

一张彩票的期望值 expected value 通常远低于其成本。

5.The game designer used expected value 期望值 to balance the rewards in the game.

游戏设计师使用期望值 expected value 来平衡游戏中的奖励。

作文

In the realm of statistics and probability, the concept of expected value plays a crucial role in decision-making processes. The expected value is essentially a measure that provides the average outcome of a random variable when an experiment is repeated many times. It serves as a fundamental tool for evaluating risks and making informed choices in uncertain situations. Understanding the expected value can greatly enhance our ability to navigate through various scenarios, whether in gambling, finance, or everyday life.To illustrate the significance of expected value, let's consider a simple example involving a game of chance. Imagine a game where you flip a coin, and if it lands on heads, you win $10; if it lands on tails, you lose $5. The expected value of this game can be calculated by considering the probabilities of each outcome. The probability of getting heads is 0.5, and the probability of getting tails is also 0.5. Therefore, the expected value can be computed as follows:Expected Value = (Probability of Heads * Amount Won) + (Probability of Tails * Amount Lost)Substituting the values, we have:Expected Value = (0.5 * 10) + (0.5 * -5) = 5 - 2.5 = 2.5.This means that, on average, you can expect to win $2.5 every time you play this game. Knowing the expected value allows players to make rational decisions about whether to participate in the game or not. If the expected value is positive, it indicates a favorable outcome in the long run, while a negative expected value suggests that the player would likely lose money over time.The application of expected value extends beyond games of chance. In finance, investors often use this concept to assess potential investments. For instance, when evaluating a stock, an investor might look at the expected value of future cash flows generated by the company. By estimating the probabilities of different outcomes, such as high growth, moderate growth, or decline, the investor can calculate the expected value of the investment. This helps them determine whether the potential return justifies the risk associated with the investment.Moreover, the expected value is also utilized in various fields such as insurance, economics, and even healthcare. Insurance companies calculate the expected value of claims to set premiums appropriately. In economics, policymakers may analyze the expected value of different policy options to choose the one that maximizes social welfare. In healthcare, decision-makers might evaluate the expected value of different treatment options based on their effectiveness and costs.In conclusion, the concept of expected value is vital for making informed decisions in uncertain situations. By providing a mathematical framework to evaluate outcomes, it empowers individuals and organizations to navigate risks more effectively. Whether in games, investments, or policy-making, understanding the expected value can lead to better decision-making and improved results. As we continue to face uncertainties in various aspects of our lives, mastering the concept of expected value will undoubtedly serve us well in our endeavors.

在统计学和概率论的领域中，期望值这一概念在决策过程中扮演着至关重要的角色。期望值本质上是一个度量，它提供了随机变量在多次实验中所产生的平均结果。它作为评估风险和在不确定情况下做出明智选择的基本工具。理解期望值可以极大增强我们在各种场景中导航的能力，无论是在赌博、金融还是日常生活中。为了说明期望值的重要性，让我们考虑一个简单的机会游戏的例子。想象一下一个游戏，你翻一枚硬币，如果它正面朝上，你赢得10美元；如果它反面朝上，你损失5美元。这个游戏的期望值可以通过考虑每个结果的概率来计算。得到正面的概率是0.5，得到反面的概率也是0.5。因此，期望值可以这样计算：期望值 = （正面概率 * 赢得金额） + （反面概率 * 损失金额）代入数值，我们有：期望值 = (0.5 * 10) + (0.5 * -5) = 5 - 2.5 = 2.5。这意味着，平均而言，每次你玩这个游戏时，可以期待赢得2.5美元。知道期望值使玩家能够理性地决定是否参与游戏。如果期望值是正的，这表明从长远来看结果是有利的，而负的期望值则表明玩家可能会随着时间的推移而亏损。期望值的应用超越了机会游戏。在金融领域，投资者经常利用这一概念来评估潜在的投资。例如，在评估一只股票时，投资者可能会关注公司未来现金流的期望值。通过估计不同结果的概率，例如高增长、中等增长或下降，投资者可以计算出投资的期望值。这帮助他们判断潜在回报是否值得与投资相关的风险。此外，期望值还被广泛应用于保险、经济学甚至医疗保健等多个领域。保险公司计算索赔的期望值以适当设定保费。在经济学中，政策制定者可能会分析不同政策选项的期望值，以选择最大化社会福利的方案。在医疗保健中，决策者可能会根据不同治疗选项的有效性和成本评估其期望值。总之，期望值的概念对于在不确定情况下做出明智的决策至关重要。通过提供评估结果的数学框架，它使个人和组织能够更有效地应对风险。无论是在游戏、投资还是政策制定中，理解期望值都能导致更好的决策和改进的结果。随着我们在生活的各个方面继续面临不确定性，掌握期望值的概念无疑将为我们的努力服务。