mathematical expectation

简明释义

数学期望

英英释义

例句

1.In probability theory, the mathematical expectation 数学期望 of a random variable gives us the long-term average value.

在概率论中，随机变量的mathematical expectation 数学期望 为我们提供了长期平均值。

2.The mathematical expectation 数学期望 of rolling a fair six-sided die is 3.5.

掷一个公平的六面骰子的mathematical expectation 数学期望 是3.5。

3.When calculating risks, businesses often rely on the mathematical expectation 数学期望 of potential outcomes.

在计算风险时，企业通常依赖于潜在结果的mathematical expectation 数学期望。

4.The mathematical expectation 数学期望 can help investors assess the average return on their investments.

mathematical expectation 数学期望 可以帮助投资者评估其投资的平均回报。

5.In game theory, players often calculate the mathematical expectation 数学期望 of their strategies to maximize gains.

在博弈论中，玩家通常计算策略的mathematical expectation 数学期望 以最大化收益。

作文

Mathematics is a fascinating field that extends beyond numbers and equations; it encompasses a wide range of concepts that help us understand the world around us. One such concept is mathematical expectation, which plays a crucial role in probability theory and statistics. The mathematical expectation (或称为期望值) of a random variable provides a measure of the central tendency of the variable's possible values, weighted by their probabilities. In simpler terms, it gives us an average outcome we can expect if we were to repeat an experiment many times. To illustrate, consider a simple game where you roll a fair six-sided die. Each face of the die has an equal chance of landing face-up, specifically a probability of 1/6. The possible outcomes are the numbers 1 through 6. To find the mathematical expectation of this die roll, we calculate the average of these outcomes, weighted by their probabilities. This can be done using the formula: E(X) = Σ [x * P(x)] where E(X) is the mathematical expectation, x represents each outcome, and P(x) is the probability of that outcome. For our die, this calculation would look like this: E(X) = (1 * 1/6) + (2 * 1/6) + (3 * 1/6) + (4 * 1/6) + (5 * 1/6) + (6 * 1/6) = 1/6 + 2/6 + 3/6 + 4/6 + 5/6 + 6/6 = 21/6 = 3.5. Thus, the mathematical expectation of rolling a six-sided die is 3.5. This means that if you were to roll the die a large number of times, the average of all your rolls would approach 3.5. The concept of mathematical expectation is not only limited to games of chance; it also has practical applications in various fields, including economics, finance, and decision-making. For instance, investors often use the mathematical expectation to evaluate potential returns on investments. By calculating the expected value of different investment options, they can make more informed decisions about where to allocate their resources. Moreover, the mathematical expectation can help in risk assessment. By understanding the expected outcomes associated with different risks, individuals and organizations can develop strategies to mitigate those risks effectively. This is especially important in fields such as insurance, where companies must predict the likelihood of claims and set premiums accordingly. In conclusion, the concept of mathematical expectation is a powerful tool that allows us to make sense of uncertainty and randomness in various contexts. Whether we are rolling dice, investing in stocks, or assessing risks, understanding the mathematical expectation helps us navigate complex situations and make better decisions. As we continue to explore the vast landscape of mathematics, concepts like mathematical expectation remind us of the importance of analytical thinking and the beauty of quantitative reasoning.

数学是一个迷人的领域，它不仅仅涉及数字和方程式；它包含了许多帮助我们理解周围世界的概念。其中一个概念是数学期望，它在概率论和统计学中发挥着至关重要的作用。随机变量的数学期望提供了一个度量，该度量表示变量可能值的集中趋势，按其概率加权。简单来说，它给出了如果我们重复实验多次，可以期待的平均结果。为了说明这一点，考虑一个简单的游戏，你掷一个公平的六面骰子。骰子的每一面都有相等的机会朝上，具体的概率为1/6。可能的结果是1到6的数字。要找到这个掷骰子的数学期望，我们计算这些结果的平均值，并按其概率加权。这可以通过以下公式完成：E(X) = Σ [x * P(x)]其中E(X)是数学期望，x表示每个结果，而P(x)是该结果的概率。对于我们的骰子，这个计算看起来是这样的：E(X) = (1 * 1/6) + (2 * 1/6) + (3 * 1/6) + (4 * 1/6) + (5 * 1/6) + (6 * 1/6)= 1/6 + 2/6 + 3/6 + 4/6 + 5/6 + 6/6= 21/6= 3.5。因此，掷一个六面骰子的数学期望是3.5。这意味着如果你掷骰子很多次，你所有掷出的平均值将接近3.5。数学期望的概念不仅限于机会游戏；它在经济学、金融和决策制定等多个领域也有实际应用。例如，投资者通常利用数学期望来评估潜在的投资回报。通过计算不同投资选项的预期值，他们可以更明智地决定在哪里分配资源。此外，数学期望可以帮助进行风险评估。通过理解与不同风险相关的预期结果，个人和组织可以有效地制定减轻这些风险的策略。这在保险等领域尤其重要，在这些领域，公司必须预测索赔的可能性并相应地设定保费。总之，数学期望的概念是一个强大的工具，它使我们能够在各种背景下理解不确定性和随机性。无论我们是在掷骰子、投资股票还是评估风险，理解数学期望有助于我们驾驭复杂的情况并做出更好的决策。当我们继续探索数学的广阔领域时，像数学期望这样的概念提醒我们分析思维的重要性以及定量推理的美丽。