uniform distribution

简明释义

均匀分布

英英释义

例句

1.When randomly selecting a card from a standard deck, the probability of drawing any specific card is based on a uniform distribution (均匀分布).

从一副标准扑克牌中随机抽取一张牌时，抽到任何特定牌的概率基于均匀分布。

2.The time it takes for a bus to arrive at a stop can be modeled as a uniform distribution (均匀分布) if it arrives every 10 minutes.

如果公交车每10分钟到达一次，那么到达站点的时间可以建模为均匀分布。

3.In a fair six-sided die, the outcome follows a uniform distribution (均匀分布) where each number has an equal probability of 1/6.

在一个公平的六面骰子中，结果遵循均匀分布，每个数字的概率都是1/6。

4.In statistics, a sample taken from a uniform distribution (均匀分布) will have all values equally likely to occur.

在统计学中，从均匀分布中抽取的样本将使所有值都有相等的发生可能性。

5.The random placement of points in a square can be modeled using a uniform distribution (均匀分布) across the area.

在一个正方形内随机放置点可以用区域内的均匀分布进行建模。

作文

In the field of statistics and probability, the concept of uniform distribution plays a crucial role in understanding random variables and their behaviors. A uniform distribution is a type of probability distribution in which all outcomes are equally likely to occur. This means that if you were to conduct an experiment or a survey, each possible outcome has the same chance of being selected. For instance, when rolling a fair six-sided die, the probability of landing on any number from one to six is equal, thus illustrating a uniform distribution.The significance of uniform distribution extends beyond simple examples like dice rolls. It serves as a foundational concept in various fields, including computer science, engineering, and economics. In computer science, for example, algorithms often rely on uniform distribution when generating random numbers. These random numbers can be utilized in simulations, cryptography, and gaming applications. The uniformity ensures that every number generated has an equal probability of being chosen, which is essential for fairness and unpredictability in these contexts.Moreover, understanding uniform distribution is vital for data analysis. When analyzing datasets, researchers may assume a uniform distribution to simplify their models. For example, if a researcher is studying the time it takes for customers to complete a purchase, they might assume that the time is uniformly distributed between two limits. This assumption allows them to apply various statistical techniques to draw conclusions about customer behavior. However, it is important for researchers to validate this assumption, as real-world data can often deviate from a true uniform distribution.In addition to its applications in research and technology, the concept of uniform distribution can also be observed in everyday life. Consider the process of selecting a random card from a standard deck of playing cards. Each card has an equal chance of being selected, demonstrating a uniform distribution among the 52 cards. This principle of equal likelihood is what makes games of chance fair and enjoyable.Despite its straightforward nature, the uniform distribution can sometimes lead to misconceptions. People may mistakenly believe that just because outcomes are uniformly distributed, they will appear evenly spaced over time. For example, if you flip a coin multiple times, you might expect to see an even distribution of heads and tails after a certain number of flips. However, due to the inherent randomness of each flip, you might end up with streaks of the same outcome. This phenomenon highlights the importance of understanding the difference between theoretical distributions and actual results.In conclusion, the uniform distribution is a fundamental concept in probability and statistics that illustrates the principle of equal likelihood among outcomes. Its implications reach far beyond basic examples, influencing various fields such as computer science, data analysis, and everyday activities. By grasping the essence of uniform distribution, individuals can better understand randomness and apply this knowledge in practical situations. Whether in research, technology, or casual games, the concept remains a key element in the study of probability and its applications.

在统计学和概率论领域，均匀分布的概念在理解随机变量及其行为方面发挥着至关重要的作用。均匀分布是一种概率分布类型，其中所有结果发生的可能性是相等的。这意味着如果你进行实验或调查，每个可能的结果都有相同的被选择的机会。例如，当掷一个公平的六面骰子时，落在一到六之间的任何数字的概率都是相等的，从而说明了均匀分布。均匀分布的重要性超越了像掷骰子这样的简单例子。它在计算机科学、工程学和经济学等多个领域作为基础概念发挥着作用。在计算机科学中，例如，算法通常依赖于均匀分布来生成随机数。这些随机数可以用于模拟、密码学和游戏应用。均匀性确保每个生成的数字都有相同的被选择的概率，这对于这些背景下的公平性和不可预测性至关重要。此外，理解均匀分布对于数据分析也至关重要。在分析数据集时，研究人员可能会假设某个变量呈现均匀分布以简化他们的模型。例如，如果研究人员正在研究客户完成购买所需的时间，他们可能会假设这个时间在两个限制之间是均匀分布的。这个假设使他们能够应用各种统计技术来得出关于客户行为的结论。然而，研究人员必须验证这一假设，因为现实世界的数据往往会偏离真实的均匀分布。除了在研究和技术中的应用，均匀分布的概念也可以在日常生活中观察到。考虑从一副标准的扑克牌中随机选择一张牌的过程。每张牌都有相同的被选择的机会，展示了52张牌之间的均匀分布。这种平等的可能性原则使得机会游戏公平且令人愉快。尽管其性质简单，但均匀分布有时会导致误解。人们可能错误地认为，仅仅因为结果是均匀分布的，它们在时间上就会均匀间隔出现。例如，如果你多次抛硬币，你可能会期待在一定数量的抛掷后看到正反面均匀分布。然而，由于每次抛掷的固有随机性，你可能会发现同一结果的连续出现。这一现象突显了理解理论分布和实际结果之间差异的重要性。总之，均匀分布是概率和统计中的一个基本概念，说明了结果之间的平等可能性原则。其影响远远超出了基本示例，影响着计算机科学、数据分析和日常活动等多个领域。通过掌握均匀分布的本质，个人可以更好地理解随机性，并在实际情况下应用这一知识。无论是在研究、技术还是休闲游戏中，这一概念仍然是概率研究及其应用的关键要素。