hypergeometric distribution

简明释义

超几何分布;

英英释义

例句

1.In quality control, the probability of finding a certain number of defective items in a sample can be modeled using the hypergeometric distribution.

在质量控制中，找到样本中一定数量的缺陷品的概率可以用超几何分布建模。

2.The hypergeometric distribution is useful in scenarios where sampling is done without replacement.

在不放回抽样的情况下，超几何分布是非常有用的。

3.Researchers often use the hypergeometric distribution to analyze the success rates of drug trials with limited samples.

研究人员经常使用超几何分布来分析有限样本的药物试验成功率。

4.When determining the likelihood of selecting a specific number of successes in a lottery, the hypergeometric distribution provides a precise calculation.

在确定在彩票中选择特定数量成功的可能性时，超几何分布提供了精确的计算。

5.A common application of the hypergeometric distribution is in card games, where you want to calculate the probability of drawing certain cards from a deck.

在纸牌游戏中，计算从一副牌中抽到特定牌的概率是超几何分布的一个常见应用。

作文

The concept of probability is fundamental in various fields, including statistics, finance, and science. One important distribution that often comes up in statistical analysis is the hypergeometric distribution. This distribution is particularly useful when dealing with scenarios where we are sampling without replacement from a finite population. Understanding the hypergeometric distribution can provide valuable insights into the likelihood of certain outcomes occurring in a defined set of circumstances.To grasp the essence of the hypergeometric distribution, let’s consider an example. Imagine a deck of cards containing 52 cards, of which 26 are red and 26 are black. If we want to know the probability of drawing a certain number of red cards when we randomly select a few cards from this deck without putting them back, we would use the hypergeometric distribution to calculate this probability. The key here is that once a card is drawn, it is not replaced, thus affecting the outcome of subsequent draws.The hypergeometric distribution is defined by three parameters: the total number of items in the population (N), the number of success states in the population (K), and the number of draws (n). In our card example, N would be 52 (the total number of cards), K would be 26 (the number of red cards), and n could vary depending on how many cards we choose to draw.The formula for the hypergeometric distribution allows us to compute the probability of obtaining exactly k successes (in our case, red cards) in n draws. This is expressed mathematically as:P(X = k) = (C(K, k) * C(N-K, n-k)) / C(N, n)Where C(a, b) represents the binomial coefficient, which calculates the number of ways to choose b successes from a total of a items. This formula emphasizes the combinatorial nature of the hypergeometric distribution, as it accounts for the different ways we can achieve the desired outcome given the constraints of our sampling method.One of the critical aspects of the hypergeometric distribution is its application in quality control and risk assessment. For instance, manufacturers may use this distribution to determine the likelihood of finding defective items in a batch when conducting quality assurance tests. By understanding the probabilities involved, businesses can make more informed decisions about their production processes and quality control measures.In conclusion, the hypergeometric distribution plays a vital role in statistical analysis, particularly in scenarios involving sampling without replacement. Its ability to model real-world situations makes it a powerful tool for researchers and professionals alike. By mastering the principles behind the hypergeometric distribution, one can gain a deeper understanding of probability and its applications in various fields, ultimately leading to better decision-making based on statistical evidence.

概率的概念在统计学、金融和科学等多个领域中都是基础性的。一个在统计分析中经常出现的重要分布是超几何分布。当处理从有限总体中不放回抽样的场景时，这个分布特别有用。理解超几何分布可以为我们提供关于在特定情况下某些结果发生的可能性的重要见解。为了掌握超几何分布的本质，让我们考虑一个例子。想象一下一个包含52张牌的牌组，其中26张是红色的，26张是黑色的。如果我们想知道在随机选择几张牌时抽到一定数量的红牌的概率，我们就会使用超几何分布来计算这个概率。这里的关键是，一旦抽出一张牌，它就不会被放回，从而影响后续抽取的结果。超几何分布由三个参数定义：总体中的总项目数（N）、总体中的成功状态数（K）和抽样次数（n）。在我们的牌组示例中，N将是52（牌的总数），K将是26（红牌的数量），而n可以根据我们选择抽取的牌的数量而变化。超几何分布的公式允许我们计算在n次抽样中恰好获得k次成功（在我们的例子中是红牌）的概率。这在数学上表示为：P(X = k) = (C(K, k) * C(N-K, n-k)) / C(N, n)其中C(a, b)表示二项式系数，它计算从a个项目中选择b个成功的方式的数量。这个公式强调了超几何分布的组合性质，因为它考虑了在我们的抽样方法的限制下实现所需结果的不同方式。超几何分布的一个关键方面是它在质量控制和风险评估中的应用。例如，制造商可能会使用这个分布来确定在进行质量保证测试时发现批次中有缺陷物品的可能性。通过理解涉及的概率，企业可以更明智地做出关于其生产过程和质量控制措施的决策。总之，超几何分布在统计分析中扮演着重要角色，特别是在涉及不放回抽样的场景中。它能够建模现实世界的情况，使其成为研究人员和专业人士的强大工具。通过掌握超几何分布背后的原则，人们可以更深入地理解概率及其在各个领域的应用，最终基于统计证据做出更好的决策。