概率论英文解释翻译、概率论的近义词、反义词、例句

英语翻译：

【计】 probability theory
【经】 probability theory; theory of probability

例句：

费马，皮尔·德1601－1665法国数学家，他有系统地阐述了现代数理论和概率论
French mathematician who formulated modern number theory and probability theory.

分词翻译：

概率的英语翻译：

probability
【化】 probability
【医】 probability
【经】 probability

论的英语翻译：

determine; discuss; in terms of; ism; statement; talk about; theory; view

网络扩展解释

概率论是数学的一个分支，主要研究随机现象的定量规律性。它通过数学模型描述不确定性事件发生的可能性，并为预测和决策提供理论依据。以下是详细解析：

一、核心概念

随机试验
指结果无法预先确定但所有可能结果已知的试验，如抛硬币、骰子投掷。
样本空间（Ω）
所有可能结果的集合，例如抛骰子的样本空间为{1,2,3,4,5,6}。
概率公理
由柯尔莫哥洛夫提出：
- 非负性：$P(A) geq 0$
- 规范性：$P(Ω)=1$
- 可加性：互斥事件概率可加

二、研究方法

古典概率
适用于等可能结果，公式：
$$P(A)=frac{text{有利结果数}}{text{总结果数}}$$
频率学派
通过长期重复试验的稳定频率定义概率。
贝叶斯概率
引入先验概率，通过观测数据更新为后验概率。

三、应用领域

统计学：数据抽样与推断
机器学习：分类器设计（如朴素贝叶斯）
金融工程：风险评估与期权定价
量子物理：粒子行为概率描述

四、现代发展

随着大数据和人工智能的兴起，概率论与信息论、优化理论的交叉应用日益增多，例如概率图模型、蒙特卡洛方法等。

如需更深入的数学推导或具体案例说明，可提供具体研究方向进一步探讨。

网络扩展解释二

概率论

概率论中文拼音为gài lǜ lùn，它是一门研究随机事件及其规律性的数学分支。

英语解释翻译

Probability Theory

Probability theory is a branch of mathematics that deals with random events and their regularity.

英文读音

/ˌprɒbəˈbɪlɪti θɪəri/

英文用法

Probability theory is used in various fields, including statistics, physics, economics, computer science, and more. It enables us to estimate the likelihood of certain events happening and the degree of confidence we can have in our estimates.

英文例句

Probability theory can help us predict the outcome of a coin toss.
In finance, probability theory is used to price options and other financial derivatives.
Quantum mechanics relies heavily on probability theory to describe the behavior of subatomic particles.
The principles of probability theory can be applied to real-life situations, such as weather forecasting and medical diagnosis.

英文近义词

Statistics：a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data.
Stochastic processes：a collection of random variables that describe the evolution of a system over time.
Randomness：the lack of pattern or predictability in events.

英文反义词

Determinism：the belief that all events, including human actions, are ultimately determined by causes external to the will.
Certainty：the state of being completely sure of something.
Prediction：an act of forecasting or stating in advance what will happen in the future.

英文单词常用度

Probability theory is a highly technical topic, and as such, its use and discussion are largely confined to academic and professional circles. However, it is a fundamental concept in many fields and is likely to surface in popular science books and articles on a regular basis.