expected value

简明释义

期望值

英英释义

例句

1.Investors often calculate the expected value 期望值 of an investment to assess its potential return.

投资者通常计算投资的 期望值 expected value 来评估其潜在回报。

2.When making decisions, it's important to consider the expected value 期望值 of different options.

在做决策时，考虑不同选项的 期望值 expected value 是很重要的。

3.The expected value 期望值 of a game can help players strategize their moves effectively.

游戏的 期望值 expected value 可以帮助玩家有效地制定策略。

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

在赌博中，期望值 expected value 可以帮助玩家判断下注是否值得冒险。

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

彩票的 期望值 expected value 通常远低于其成本。

作文

The concept of expected value is fundamental in statistics and probability theory. It provides a way to quantify the average outcome of a random variable, which can be incredibly useful in various fields such as economics, finance, and decision-making. In simple terms, the expected value is the long-term average or mean of a random variable's possible values, weighted by their probabilities. Understanding this concept can help individuals make informed decisions based on potential outcomes.To illustrate the idea of expected value, let’s consider a simple example involving a game of chance. Imagine you are playing a lottery where you can win $100 with a probability of 0.1 (or 10%), and you lose $10 with a probability of 0.9 (or 90%). To calculate the expected value of playing this lottery, we would multiply each outcome by its respective probability and then sum these products:1. Winning scenario: $100 * 0.1 = $102. Losing scenario: -$10 * 0.9 = -$9Now, we add these two results together:$10 + (-$9) = $1.This means that the expected value of playing this lottery is $1. In other words, if you played this lottery many times, you would expect to gain an average of $1 per play in the long run. This insight can guide your decision about whether or not to participate in the lottery.In a broader context, the notion of expected value can be applied to various real-life scenarios. For instance, investors often use expected value calculations to assess the potential profitability of different investment options. By analyzing the possible returns and their associated probabilities, they can determine which investments are likely to yield the best overall returns over time.Moreover, businesses frequently employ expected value analysis when making strategic decisions. For example, a company may evaluate the potential outcomes of launching a new product. They would estimate the revenue from successful sales against the costs incurred if the product fails. By calculating the expected value of launching the product, they can weigh the risks and benefits more effectively.In the realm of everyday life, understanding expected value can also enhance personal decision-making. When faced with choices that involve uncertainty—such as whether to buy insurance or gamble—individuals can use expected value to analyze the potential benefits and drawbacks. This approach encourages a more rational evaluation of options rather than relying solely on intuition or emotion.Despite its usefulness, it is important to recognize the limitations of expected value. It assumes that all outcomes are known and that probabilities can be accurately estimated. In reality, uncertainties abound, and unforeseen events can significantly alter outcomes. Therefore, while expected value can provide valuable insights, it should be used alongside other analytical tools and considerations.In conclusion, the concept of expected value serves as a powerful tool in understanding and navigating uncertain situations. Whether in gambling, investing, business strategy, or daily decision-making, grasping the expected value allows individuals to make more informed choices based on statistical reasoning. As we continue to encounter complex decisions in our lives, the ability to apply the principles of expected value will undoubtedly prove beneficial in achieving favorable outcomes.

“期望值”这一概念在统计学和概率论中是基础性的。它提供了一种量化随机变量平均结果的方法，这在经济学、金融和决策制定等多个领域都极为有用。简单来说，期望值是随机变量可能值的长期平均或均值，按其概率加权。理解这个概念可以帮助个人根据潜在结果做出明智的决策。为了说明期望值的概念，我们来考虑一个简单的例子，涉及一个机会游戏。想象一下你在玩一个彩票，你有10%的概率赢得100美元，而有90%的概率损失10美元。为了计算玩这个彩票的期望值，我们将每个结果乘以其相应的概率，然后将这些乘积相加：1. 赢得场景：100美元 * 0.1 = 10美元2. 失去场景：-10美元 * 0.9 = -9美元现在，我们将这两个结果相加：10美元 + (-9美元) = 1美元。这意味着玩这个彩票的期望值是1美元。换句话说，如果你多次参与这个彩票，你预计每次游戏的平均收益为1美元。这一见解可以指导你决定是否参与彩票。在更广泛的背景下，期望值的概念可以应用于各种现实生活场景。例如，投资者经常使用期望值计算来评估不同投资选项的潜在盈利能力。通过分析可能的回报及其相关概率，他们可以确定哪些投资在长期内可能产生最佳整体回报。此外，企业在制定战略决策时也经常采用期望值分析。例如，一家公司可能会评估推出新产品的潜在结果。他们会估算成功销售的收入与产品失败时发生的成本。通过计算推出产品的期望值，他们可以更有效地权衡风险和收益。在日常生活中，理解期望值也可以提升个人决策能力。当面临涉及不确定性的选择时——例如是否购买保险或赌博——个人可以使用期望值来分析潜在的利弊。这种方法鼓励对选择进行更理性的评估，而不仅仅依赖直觉或情感。尽管期望值非常有用，但重要的是要认识到它的局限性。它假设所有结果都是已知的，并且概率可以被准确估计。在现实中，不确定性无处不在，意想不到的事件可能会显著改变结果。因此，虽然期望值可以提供有价值的见解，但它应该与其他分析工具和考虑因素一起使用。总之，期望值的概念作为理解和应对不确定情况的强大工具。无论是在赌博、投资、商业策略还是日常决策中，掌握期望值使个人能够基于统计推理做出更明智的选择。随着我们在生活中继续面临复杂的决策，运用期望值原则的能力无疑会在实现有利结果方面证明其价值。