exponential distribution

简明释义

指数分布

英英释义

例句

1.The waiting time for a customer to be served in a queue can be represented by an exponential distribution 指数分布.

顾客在排队时等待服务的时间可以用指数分布 exponential distribution表示。

2.The time between arrivals of buses can be modeled using an exponential distribution 指数分布.

公交车到达之间的时间可以用指数分布 exponential distribution来建模。

3.The decay of radioactive particles follows an exponential distribution 指数分布.

放射性粒子的衰变遵循指数分布 exponential distribution。

4.In telecommunications, the time until the next packet arrives can be modeled with an exponential distribution 指数分布.

在电信中，直到下一个数据包到达的时间可以用指数分布 exponential distribution建模。

5.In reliability engineering, the lifespan of a light bulb is often described by an exponential distribution 指数分布.

在可靠性工程中，灯泡的寿命通常用指数分布 exponential distribution来描述。

作文

The concept of exponential distribution is fundamental in the field of statistics and probability. It describes the time between events in a process where events occur continuously and independently at a constant average rate. Understanding this distribution can provide valuable insights into various real-world phenomena, particularly in fields such as telecommunications, finance, and natural sciences.To illustrate the significance of exponential distribution, consider a scenario involving customer service. Suppose a call center receives an average of five calls per hour. The time between incoming calls can be modeled using an exponential distribution. This means that while the average time between calls is twelve minutes, the actual time can vary significantly. Some calls may come in quick succession, while others may have longer gaps in between. This variability is a key characteristic of the exponential distribution, which is often used to model waiting times or lifetimes of objects.One of the defining features of the exponential distribution is its memoryless property. This property states that the probability of an event occurring in the future is independent of any past events. For instance, if a customer has been waiting for ten minutes already, the probability that they will have to wait an additional five minutes remains the same as it was when they first arrived. This unique characteristic makes the exponential distribution particularly useful in queuing theory, where it helps in designing efficient service systems.In addition to its applications in service industries, the exponential distribution is also prevalent in reliability engineering. Engineers use it to model the lifespan of products and components. For example, if a light bulb has a mean lifetime of 1,000 hours, the time until failure can be modeled with an exponential distribution. This allows manufacturers to predict how long a batch of bulbs will last on average, helping them to manage inventory and warranty claims effectively.Moreover, the exponential distribution is not limited to just theoretical applications; it has practical implications too. In finance, for example, the time until a stock reaches a certain price can be modeled using an exponential distribution. Investors can use this information to make informed decisions about buying and selling stocks based on expected timeframes.In conclusion, the exponential distribution is a powerful statistical tool that helps us understand and model the timing of events. Whether in customer service, reliability engineering, or finance, its applications are vast and varied. By grasping the principles behind the exponential distribution, we can better analyze data and make predictions that inform our decisions in both professional and everyday contexts. As we continue to explore the complexities of probability and statistics, the exponential distribution will undoubtedly remain a key concept that shapes our understanding of random processes and their implications in the real world.

在统计学和概率论领域，指数分布的概念是基础性的重要内容。它描述了在一个过程中事件之间的时间，这些事件以恒定的平均速率持续独立地发生。理解这种分布可以为我们提供对各种现实世界现象的有价值的洞察，特别是在电信、金融和自然科学等领域。为了说明指数分布的重要性，考虑一个涉及客户服务的场景。假设一个呼叫中心每小时接到五个电话。来电之间的时间可以用指数分布来建模。这意味着，虽然来电之间的平均时间是十二分钟，但实际的时间可能会有很大的变化。有些电话可能会迅速接连而来，而其他电话之间可能会有更长的间隔。这种变异性是指数分布的一个关键特征，通常用于建模等待时间或物体的寿命。指数分布的一个定义特征是它的无记忆性。这个特性表明，未来事件发生的概率与任何过去事件是独立的。例如，如果一位客户已经等了十分钟，那么他们需要再等五分钟的概率与他们第一次到达时的概率是相同的。这一独特特性使得指数分布在排队理论中尤为有用，它帮助设计高效的服务系统。除了在服务行业的应用外，指数分布在可靠性工程中也很常见。工程师使用它来建模产品和组件的寿命。例如，如果一个灯泡的平均寿命为1000小时，那么故障前的时间可以用指数分布来建模。这使得制造商能够预测一批灯泡的平均使用时间，帮助他们有效管理库存和保修索赔。此外，指数分布不仅限于理论应用；它也具有实际意义。例如，在金融领域，股票达到某一价格的时间可以用指数分布来建模。投资者可以利用这些信息，根据预期的时间框架做出有关买卖股票的明智决策。总之，指数分布是一种强大的统计工具，帮助我们理解和建模事件的时机。无论是在客户服务、可靠性工程还是金融领域，其应用范围广泛且多样。通过掌握指数分布背后的原理，我们可以更好地分析数据并做出影响我们职业和日常生活决策的预测。当我们继续探索概率和统计的复杂性时，指数分布无疑将继续成为塑造我们对随机过程及其在现实世界中影响的理解的关键概念。