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所在平台: Udemy |
课程主页: https://www.udemy.com/course/statistics-king-abdulaziz-university/
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**课程名称：** 概率与统计：为工程师和科学家量身定制 (Walpole) **课程概述：** 本课程深入探讨工程统计学和概率论的理论与实际应用，旨在帮助学员将这些知识应用于解决真实的商业问题。课程内容结构清晰，包含丰富的案例研究、随堂测验和阶段性评估。通过高清专业视频，学员将学会如何将所学知识应用于实际的工程和科学领域。 **课程重点内容：** * **统计学与概率论导论：** * 为何学习统计学 * 数据类型 * 总体、单元与样本的定义 * 随机数表生成 * 参数与统计量的区别 * 统计学分支 (描述统计与推断统计) * **描述统计工具：** * 帕累托图 * 点图 * 散点图 * 频率分布 * 直方图 * 茎叶图 * 集中趋势测量 (均值、中位数、众数) * 离散趋势测量 (极差、方差、标准差) * 加权平均数 * 分组数据的标准差 * 变异系数 * **概率论基础：** * 概率实验、结果、样本空间与事件的定义 * 概率类型 (古典概率、经验概率、主观概率) * 事件组合 * 计数原理 (乘法原理、排列、组合) * 概率公理 * 文氏图 * 加法法则 * 互斥事件 * 条件概率 * 乘法法则 * 独立事件 * 贝叶斯定理 * **概率分布：** * 随机变量类型 * 离散概率分布 (DPD) * 二项分布 * 超几何分布 * 泊松分布 * DPD 的均值、方差与标准差 * 连续概率分布 * 正态分布 * 标准正态分布 * 标准正态分布表 * 正态分布对二项分布的近似 * **抽样分布：** * 总体与样本 * 样本均值的抽样分布 * (σ 已知) -> z 分布 * (σ 未知) -> t 分布 * 样本方差的抽样分布 -> χ² 分布 * F 分布 * **总体参数估计：** * 总体均值的估计 * 点估计 * 区间估计 (n≥30 或正态总体，s 未知) * 样本容量计算 * **假设检验：** * 假设检验导论 * 第一类与第二类错误 * 显著性水平 * 假设检验流程：检验统计量选择、统计决策 * 总体均值假设检验： * 大样本 (n≥30 或正态总体，σ 已知) -> z 检验 * 小样本 (n<30 且正态总体，σ 未知) -> t 检验 * 利用 P 值进行假设检验 * 比例的假设检验 * **相关与回归：** * 相关系数 r * 散点图 * 相关系数 (使用协方差计算) * 线性回归 * 回归直线 * 变量的线性组合 * 协方差 本课程还将涵盖更多与工程和科学应用相关的统计学和概率论主题。
Welcome to Engineering Statistics and Probability TheoryThis course will go over theories and implementation of engineering statistics and probability theories to real business problems. Each section has many examples, quizzes, and assessment exams.Our course includes professional HD Videos with extensive case studies to show you how to apply this knowledge to solve real and practical problems.In this course we will cover:Introduction to statistics and probabilityWhy Study Statistics?Types of dataDefinitions: Populations, units, and SampleGeneration of random number tableThe difference between Parameters & StatisticsBranches of Statistics (Descriptive and Inferential statistics)Pareto chartDot plotScatter plotFrequency distributionHistogramStem and Leaf displayMeasures of Central Tendency (Mean, Median, and Mode)Measures of Variation (Range, Variance and Standard Deviation)Weighted MeanStandard Deviation for Grouped DataCoefficient of variationDefinitions (Probability experiment, Outcome, Sample space, and Event)Types of ProbabilityClassical (or theoretical) ProbabilityEmpirical (or statistical) ProbabilitySubjective ProbabilityCombining eventsCounting PrinciplesMultiplication of choicesPermutationCombinationThe Axioms of ProbabilityVenn diagramsThe Addition RuleMutually Exclusive EventsConditional ProbabilityThe Multiplication RuleIndependent EventsBayes' TheoremDiscrete Probability DistributionsTypes of Random VariablesDiscrete Probability Distributions (DPD)Binomial DistributionHypergeometric DistributionPoisson DistributionMean, Variance, and Standard Deviation of DPDContinuous Probability DistributionsNormal DistributionThe Standard Normal DistributionThe Standard Normal Distribution TablesThe Normal Approximation to the Binomial DistributionSampling distributionsPopulations and SamplesThe Sampling Distribution of the MeanThe Sampling Distribution of the Mean (σ Known) -> z-distributionThe Sampling Distribution of the Mean (σ Unknown) -> t-distributionSampling Distribution of the Variance -> χ2-distributionF - DistributionEstimation of Population'sEstimation of Population's MeanPoint EstimationInterval EstimationNormal (s known). Or n ³ 30Normal (s Unknown).Calculation of Sample SizeTests of HypothesesIntroduction to Hypothesis TestingType I and type II errorsLevel of SignificanceHypotheses Testing ProcessTest Statistic SelectionStatistical DecisionHypothesis Testing for the Population's Mean:Large Samples; n ≥ 30 or Normal population (σ Known) à (z)Small Samples: n < 30 and Normal population (σ Unknown) à (t)Tests of Hypotheses Using P-valueHypothesis Testing for ProportionsCorrelation and RegressionCorrelation Coefficient rscatter plotCorrelation CoefficientLinear RegressionRegression LineLinear combination of variablesCovarianceCorrelation using covarianceand much more!
