poisson distribution

简明释义

泊松分布

英英释义

例句

1.The occurrence of defects in a batch of manufactured items can be modeled with a poisson distribution (泊松分布) for quality control.

一批制造商品中的缺陷发生情况可以用poisson distribution (泊松分布) 进行建模，以进行质量控制。

2.The average number of emails received per day follows a poisson distribution (泊松分布), helping IT departments manage server load.

每天收到的电子邮件平均数量遵循poisson distribution (泊松分布)，帮助IT部门管理服务器负载。

3.A biologist studying rare species sightings might use a poisson distribution (泊松分布) to estimate population density.

一位研究稀有物种目击情况的生物学家可能会使用poisson distribution (泊松分布) 来估计种群密度。

4.Traffic accidents at a specific intersection can be analyzed using a poisson distribution (泊松分布) to improve safety measures.

特定交叉口的交通事故可以通过poisson distribution (泊松分布) 进行分析，以改善安全措施。

5.In a call center, the number of calls received in an hour can be modeled using a poisson distribution (泊松分布) to predict staffing needs.

在呼叫中心，每小时接到的电话数量可以使用poisson distribution (泊松分布) 来预测人员需求。

作文

The concept of the poisson distribution is a fundamental topic in the field of statistics and probability theory. It describes the probability of a given number of events occurring in a fixed interval of time or space, under the condition that these events happen with a known constant mean rate and are independent of the time since the last event. This distribution is named after the French mathematician Siméon Denis Poisson, who introduced it in the early 19th century. Understanding the poisson distribution is essential for various applications, ranging from telecommunications to natural sciences.One of the most common examples of the poisson distribution can be seen in the context of rare events, such as the number of phone calls received by a call center in an hour. If we know that, on average, the call center receives five calls per hour, we can use the poisson distribution to calculate the probability of receiving a specific number of calls in that hour. For instance, we might want to find out the likelihood of receiving exactly three calls. The formula for the poisson distribution is given by:P(X = k) = (λ^k * e^(-λ)) / k!,where λ is the average rate (in this case, five calls), k is the actual number of events (three calls), and e is Euler's number, approximately equal to 2.71828.Using this formula, we can compute that the probability of receiving exactly three calls is approximately 0.1008, or 10.08%. This example illustrates how the poisson distribution can help businesses plan their resources effectively, ensuring that they have enough staff to handle incoming calls without overwhelming them.In addition to its practical applications, the poisson distribution also has theoretical significance in statistics. It serves as a model for various phenomena, including the distribution of particles in physics or the occurrence of mutations in genetics. Researchers often rely on the poisson distribution when dealing with count data, particularly when the counts are low and the events are independent.Moreover, the poisson distribution is closely related to other statistical distributions. For instance, under certain conditions, if the number of trials increases while the probability of success decreases, the poisson distribution can approximate the binomial distribution. This relationship is particularly useful in scenarios where the total number of trials is large, but the probability of each individual trial resulting in success is small.In conclusion, the poisson distribution is a powerful tool in statistics that provides valuable insights into the behavior of random events. Its applications are widespread, influencing fields such as telecommunications, biology, and quality control. By mastering the poisson distribution, one can gain a deeper understanding of how to model and analyze real-world situations involving random occurrences. As we continue to explore the complexities of data and probability, the poisson distribution will undoubtedly remain a crucial component of statistical analysis and decision-making processes.

泊松分布是统计学和概率论领域的一个基本概念。它描述了在固定时间或空间间隔内发生特定事件的概率，前提是这些事件以已知的恒定平均速率发生，并且与上一个事件发生的时间无关。这个分布以法国数学家西门·德尼·泊松的名字命名，他在19世纪初引入了这一概念。理解泊松分布对各种应用至关重要，从电信到自然科学。泊松分布最常见的例子之一可以在稀有事件的背景下看到，例如一个呼叫中心在一小时内接收到的电话数量。如果我们知道呼叫中心平均每小时接到五个电话，我们可以使用泊松分布来计算在该小时内接到特定数量电话的概率。例如，我们可能想知道接到正好三个电话的可能性。泊松分布的公式如下：P(X = k) = (λ^k * e^(-λ)) / k!,其中λ是平均速率（在这种情况下为五个电话），k是实际事件的数量（三个电话），e是欧拉数，大约等于2.71828。使用这个公式，我们可以计算出接到正好三个电话的概率大约为0.1008，或10.08%。这个例子说明了泊松分布如何帮助企业有效规划资源，确保他们有足够的员工来处理来电，而不会使他们不堪重负。除了其实际应用外，泊松分布在统计学中也具有理论意义。它为各种现象提供模型，包括物理学中的粒子分布或遗传学中的突变发生。研究人员在处理计数数据时经常依赖泊松分布，特别是当计数较低且事件独立时。此外，泊松分布与其他统计分布密切相关。例如，在某些条件下，如果试验次数增加而成功概率降低，泊松分布可以近似于二项分布。这种关系在总试验次数很大但每个单独试验成功概率较小的情况下尤其有用。总之，泊松分布是统计学中的一种强大工具，为随机事件的行为提供了宝贵的见解。它的应用广泛，影响着电信、生物学和质量控制等领域。通过掌握泊松分布，人们可以更深入地理解如何建模和分析涉及随机发生的现实情况。随着我们继续探索数据和概率的复杂性，泊松分布无疑将继续成为统计分析和决策过程中的关键组成部分。