|
所在平台: Udemy |
课程主页: https://www.udemy.com/course/basic-concepts-of-probability-probability-distributions/
课程评论：没有评论
课程名称：概率与概率分布基本概念 课程概述： 概率是事件发生的机会或可能性的定义，反映了某件事情发生的程度。例如，掷硬币时，两面朝上的可能性相等。通过数字来解释 chance，若某事件必然发生，其发生概率为1（或100%）；若绝对不发生，其发生概率为0（或0%）。某事件的概率位于0≤p≤1的区间内，0表示事件绝对不发生，而1表示事件必然发生。 本课程内容包括： - 使用示例讲解概率的基本概念 - 重要的概率定理 - 至少一个事件发生的概率 - 应用联合概率和条件概率的贝叶斯定理 - 概率分布 - 在不同可能事件下通过二项分布计算概率 - 使用平均病例数的泊松分布 - 正态分布及其曲线 概率的重要性： - 概率在生物过程如遗传、进化和流行病的理解中至关重要，尤其随着基因组项目与微阵列实验所产生的数据量激增，对新概率模型的需求日益增加。 - 概率在金融领域的应用已经颠覆了这一行业，没有可靠的衍生品定价模型和风险管理，这些市场无法存在。 - 马尔科夫链蒙特卡洛方法使得复杂概率结构的平稳分布研究成为可能，对日常复杂问题的分析非常重要。 - 在计算机科学中，随机算法利用概率解决复杂问题。 - 概率理论为复杂网络的数学解释和行为预测提供了重要框架，包括互联网、电力网络、无线通信及现代制造系统等设计，也包括自然的地球物理系统。 - 当前科学研究中的许多挑战涉及随机建模、蒙特卡洛模拟和统计数据分析，这些都离不开概率工具，统计学与概率一直密不可分。 - 概率理论试图将关于事件发生或不发生的各种假设转化为形式化的量化测量。 - 多次实验后，概率结果与实际发生的情况非常接近，若进行长期平均计算。 - 在理论分布的帮助下，可以准备所有类型的频率分布，这些都是基于理论框架而准备的。 - 样本理论的基础：在某些情况下，由于成本或研究规模，无法研究整个大群体，此时基于概率理论对整体的部分进行研究并进行估算。
Probability is defined as a chance or likelihood of happening of an event. It is basically degree of likelihood that something will happen. Probability measures the likelihood that something specific will occur. For example, a tossed coin has an equal chance, or probability, of landing with one side up ("heads") or the other ("tails"). Probability uses numbers to explain chance. If something is absolutely going to happen, its probability of occurring is 1, or 100 percent. If something absolutely will not happen, its probability of occurring is 0, or 0 percent. The probability of an event is a number lying in the interval 0≤p≤1, with 0 corresponding to an event that never occurs and 1 to an event that is certain to occur. For an experiment with N equally likely outcomes the probability of an event A is n/N, where n is the number of outcomes in which the event A occursThis course comprises of: Basic concepts of Probability using illustrative examplesBasic Theorems of ProbabilityProbability of happening of atleast one eventBaye's Theorem in Probability applying Joint probability and conditional probabilityProbability DistributionsCalculation of Probability when there are various possible events using Binomial Distribution Poisson Distribution using mean number of casesNormal Distribution & Normal Distribution curvesImportance of Probability:· The probabilistic understanding of biological processes such as genetic inheritance, evolution, and epidemics, has been essential for scientific progress. The recent explosion in the amount of data from genome projects and other sources, such as microarray experiments, has led to the need for new probability models to understand both the structure of the data and the underlying biology.· The application of probability to finance has revolutionized an industry. Without the probabilistic models that provide reliable pricing of derivative securities and guide the management of associated risk, these markets could not exist.· Markov chain Monte Carlo methods allow the investigation of stationary distributions of complex probabilistic structures which are used in analyzing complex day to day problems.· In computer science, randomized algorithms using probability enable the solution of complex problems that would otherwise be inaccessible.· Probability theory provides an essential framework for mathematically interpreting and predicting the behavior of complex networks. These include both human designs such as the Internet, power networks, wireless communication, and modern manufacturing systems, as well as natural geophysical systems such as seismic, climatic and hydrologic systems.· Many current research challenges across the sciences involve a combination of modeling randomness, Monte Carlo simulation and statistical data analysis, all of which depend on probabilistic tools. In particular Statistics and Probability are and have always been inextricably linked.· The probability theory tries to put the different conjectures about the happening or not happening or not happening of an event into formal quantitative measures.· The results of probability are very near the actual happening( OR not happening) If experiments are repeated many times and a long time average is computed· Useful in theoretical distribution: With the help all types of frequency distribution can be prepared. They are prepared on theoretical basis.· Basis of the theory of sampling: Sometimes the study of a big group is not possible and the cost involved in the study is not just if able. In such cases on the basis of the theory of probability a part of the whole is studied and estimates are made.
