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所在平台: Udemy |
课程主页: https://www.udemy.com/course/advanced-statistics/
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课程名称:工程师应用统计与概率:蒙哥马利 课程概述: 本课程旨在帮助学习者掌握应用统计和概率在工程中的重要性,具体包括以下几个部分的学习目标: 1. **参数估计**:理解如何估计总体或概率分布的参数,掌握正态分布作为抽样分布的关键作用以及中心极限定理的原理。 2. **点估计的性质**:学习点估计的偏差、方差以及均方误差等重要性质,能够使用矩法和最大似然法构造点估计,并计算参数估计的精确度。 3. **置信区间构造**:掌握如何构建正态分布的均值置信区间、方差和标准差的置信区间以及总体比例的置信区间,并学会使用一般方法构造近似置信区间和预测区间。 4. **假设检验**:将工程决策问题构造为假设检验,使用Z检验或t检验对正态分布的均值进行假设检验,学习如何使用P值法做出决策,并计算检验的功效及II型错误概率。 5. **比较实验分析**:在有两个样本的比较实验中构造假设检验,测试均值差、方差比及总体比例差的假设,并构建相应的置信区间。 6. **简单线性回归**:运用简单线性回归方法建立工程和科学数据的经验模型,理解最小二乘法在回归模型参数估计中的应用。 通过本课程的学习,学员将能够深入理解并应用统计和概率理论,提升在工程领域的决策能力和分析技巧。
After careful study of this chapter, you should be able to do the following:1.Explain the general concepts of estimating the parameters of a population or a probability distribution2.Explain the important role of the normal distribution as a sampling distribution and the central limit theorem3.Explain important properties of point estimators, including bias, variances, and mean square error4.Construct point estimators using the method of moments and the method of maximum likelihood.5.Compute and explain the precision with which a parameter is estimated6.Construct a point estimator using the Bayesian approach8- After careful study of this chapter, you should be able to do the following:1.Construct confidence intervals on the mean of a normal distribution, using normal distribution or t distribution method2.Construct confidence intervals on the variance and standard deviation of normal distribution3.Construct confidence intervals on a population proportion4.Use a general method for constructing an approximate confidence interval on a parameter5.Construct a prediction interval for a future observation6.Construct a tolerance interval for a normal population7.Explain the three types of interval estimates: confidence intervals, prediction intervals, and tolerance intervals9- After careful study of this chapter, you should be able to do the following:1.Structure engineering decision-making problems as hypothesis tests2.Test hypotheses on the mean of a normal distribution using a Z-test or a t-test3.Test hypotheses on the variance or standard deviation of a normal distribution4.Test hypotheses on a population proportion5.Use the P-value approach for making decisions in hypothesis tests6.Compute power & Type II error probability and make sample size selection decisions for tests on means, variances and proportions7.Explain & use the relationship between confidence intervals & hypothesis tests8.Use the chi-square goodness-of-fit test to check distributional assumptions9.Apply contingency table tests10.Apply nonparametric tests11.Use equivalence testing12.Combine P-values10- After careful study of this chapter, you should be able to do the following:1.Structure comparative experiments involving two samples as hypothesis tests2.Test hypotheses and construct confidence intervals on the difference in means of two normal distributions3.Test hypotheses and construct confidence intervals on the ratio of the variances or standard deviations of two normal distributions4.Test hypotheses and construct confidence intervals on the difference in two population proportions5.Use the P-value approach for making decisions in hypothesis tests6.Compute power, Type II error probability, and make sample size decisions for two-sample tests on means, variances & proportions7.Explain and use the relationship between confidence intervals and hypothesis tests11- After careful study of this chapter, you should be able to do the following:1.Use simple linear regression for building empirical models to engineering and scientific data2.Understand how the method of least squares is used to estimate the parameters in a linear regression model3.Analyze residuals to determine if the regression model is an adequate fit to the data or to see if any underlying assumptions are violated4.Test the statistical hypotheses and construct confidence intervals on the regression model parameters5.Use the regression model to make a prediction of a future observation and construct an appropriate prediction interval on the future observation6.Apply the correlation model7.Use simple transformations to achieve a linear regression model