binomial

简明释义

英[baɪˈnəʊmiəl]美[baɪˈnoʊmiəl]

adj. 二项式的；双名的，二种名称的

n. 二项式；双名词组，二种名称；成对词

英英释义

单词用法

同义词

反义词

例句

1.It USES the binomial distribution to calculate the probability of getting any specific number of accidents.

保险公司就可以用二项分布公式，来计算特定数目事故发生的概率。

2.Returns the individual term binomial distribution probability.

返回一元二项式分布的概率值。

3.At present, the most commonly used methods include: Monte Carlo methods, binomial tree, finite element and finite difference methods.

目前比较成熟的数值方法有：蒙特卡罗方法，二叉树方法，有限元和有限差分方法。

4.This is nothing but the binomial expansion.

这不过是二项展开式。

5.By using this method, we deduced the probability generating function of the binomial distribution in the Markov dependent sequence.

利用这一方法推导了在马氏相关序列下的二项分布的概率函数。

6.The optimal strategies can be obtained by solve the model with binomial lattice method.

用二项式网格方法求解该模型，即可求得各阶段的最优订购策略。

7.This method can also be used for designing traditional binomial transformer, the practical examples are given.

该优化方法也可以应用于传统二项式变换器的设计中，并通过实例进行说明。

8.Based on the works of predecessors, in this paper, we introduce a continuous-state compound binomial ruin model.

本文在前人工作的基础上，考虑了状态空间连续的复合二项风险模型。

9.Basic principle of reliability evaluation of Binomial distribution unit is offered for correctly using in engineering.

为正确使用二项分布单元的可靠性评定方法提供了基础。

10.The binomial 二项式 theorem provides a way to expand expressions of the form (a + b)^n.

binomial 二项式 定理提供了一种扩展形式为 (a + b)^n 的表达式的方法。

11.In statistics, a binomial 二项式 distribution is used to model the number of successes in a fixed number of trials.

在统计学中，binomial 二项式 分布用于模拟固定次数试验中的成功次数。

12.A binomial 二项式 expression consists of two terms separated by a plus or minus sign.

一个 binomial 二项式 表达式由两个术语组成，之间用加号或减号分隔。

13.The formula for a binomial 二项式 expansion can be derived using Pascal's triangle.

可以通过帕斯卡三角形推导出 binomial 二项式 展开的公式。

14.In algebra, you often encounter binomial 二项式 coefficients when simplifying expressions.

在代数中，简化表达式时经常会遇到 binomial 二项式 系数。

作文

In mathematics, the term binomial refers to a polynomial that consists of two terms. These two terms are typically separated by a plus or minus sign. Understanding binomial expressions is fundamental in algebra and has applications in various fields such as statistics, probability, and even finance. For instance, the classic example of a binomial expression is (a + b), where 'a' and 'b' are any numbers or variables. The significance of binomial expressions extends beyond mere definitions. They form the basis of the famous binomial theorem, which provides a formula for expanding expressions that are raised to a power. The binomial theorem states that (x + y)^n can be expanded into a sum involving terms of the form C(n, k) * x^(n-k) * y^k, where C(n, k) is a binomial coefficient. This theorem is not only a critical concept in algebra but also plays a vital role in combinatorics, which is the study of counting, arrangement, and combination of objects.Moreover, binomial distributions are crucial in statistics, especially when dealing with experiments that have two possible outcomes, such as success or failure. The binomial distribution gives us the probability of obtaining a fixed number of successes in a certain number of trials, making it an essential tool in fields like quality control, risk assessment, and even sports analytics. To illustrate the practical application of binomial concepts, consider a simple example: flipping a coin. If we flip a coin three times, we can use the binomial distribution to determine the probability of getting exactly two heads. Here, the number of trials is three, the number of successes is two, and the probability of success on each trial (getting heads) is 0.5. Using the binomial formula, we can calculate this probability and gain insights into the likelihood of different outcomes. Furthermore, binomial expressions are often encountered in real-life situations. For example, when calculating the area of rectangles, the formula A = length * width can be expressed in binomial form if we consider changing dimensions. This flexibility shows how binomial concepts permeate various aspects of life, from basic arithmetic to complex statistical analyses. In conclusion, mastering the concept of binomial is essential for anyone studying mathematics or related fields. Its applications are vast and varied, from theoretical explorations in algebra to practical uses in statistics and probability. By understanding binomial expressions and their properties, students and professionals alike can enhance their analytical skills and apply these concepts to solve real-world problems effectively. In summary, the term binomial represents more than just a mathematical definition; it embodies a rich framework of ideas that are integral to numerous disciplines. Whether one is engaged in academic pursuits or everyday problem-solving, the principles surrounding binomial expressions will undoubtedly prove beneficial.

在数学中，术语binomial指的是由两个项组成的多项式。这两个项通常由加号或减号分隔。理解binomial表达式是代数的基础，并且在统计学、概率论甚至金融等多个领域都有应用。例如，经典的binomial表达式的例子是(a + b)，其中'a'和'b'可以是任何数字或变量。binomial表达式的重要性超越了简单的定义。它们构成了著名的二项式定理的基础，该定理提供了一个公式，用于展开提升到某个幂的表达式。二项式定理表明，(x + y)^n可以展开为涉及形式为C(n, k) * x^(n-k) * y^k的项的总和，其中C(n, k)是二项式系数。这个定理不仅是代数中的关键概念，而且在组合数学中也起着重要作用，组合数学是研究对象的计数、排列和组合的学科。此外，binomial分布在统计学中至关重要，特别是在处理具有两种可能结果的实验时，例如成功或失败。binomial分布给我们提供了在一定数量的试验中获得固定数量成功的概率，使其成为质量控制、风险评估甚至体育分析等领域的重要工具。为了说明binomial概念的实际应用，考虑一个简单的例子：抛硬币。如果我们抛硬币三次，我们可以使用binomial分布来确定恰好得到两个正面的概率。在这里，试验的次数是三次，成功的次数是两次，每次试验成功的概率（得到正面）是0.5。使用binomial公式，我们可以计算这个概率，从而获得不同结果的可能性。此外，binomial表达式经常出现在现实生活中。例如，在计算矩形的面积时，公式A = 长度 * 宽度可以用binomial形式表示，如果我们考虑变化的尺寸。这种灵活性显示了binomial概念如何渗透到生活的各个方面，从基本的算术到复杂的统计分析。总之，掌握binomial的概念对于任何学习数学或相关领域的人来说都是至关重要的。它的应用范围广泛而多样，从代数的理论探索到统计和概率的实际用途。通过理解binomial表达式及其属性，学生和专业人士都可以增强他们的分析技能，并有效地将这些概念应用于解决现实问题。总结来说，术语binomial代表的不仅仅是一个数学定义；它体现了一套丰富的思想框架，这些框架在众多学科中都是不可或缺的。无论一个人从事学术研究还是日常问题解决，围绕binomial表达式的原则无疑会证明是有益的。