Stat 560: Introduction to Mathematical Statistics
Ramón V. León

Contents

Course Topics*. 1

Enrichment Topics. 1

 

Course Topics*

 

1.       What is Statistics

2.       The Nature of Data

3.       Reliability and Maintainability Data:  Complete and Censored Data

4.       Opinion Polls and Confidence Intervals for Proportions

5.       Distributions: Normal, Weibull, Lognormal and Gamma

6.       Confidence Intervals for Distribution Functions

7.       Displaying and Summarizing Categorical Data

8.       Displaying and Summarizing Quantitative Data

9.       Comparing Distributions

10.   Standard Deviation and the Normal Distribution

11.   Central Limit Theorem

12.   Confidence Intervals for the Mean

13.   Bootstrap Confidence Intervals for the Mean

14.   Prediction and Tolerance Intervals

15.   Comparative Experiments and Observational Data

16.   Confidence Intervals for the Difference of Proportions

17.   Confidence Intervals for the Difference of Two Means: Independent Samples

18.   Bootstrap Confidence Intervals for the Difference of Two Means: Independent Samples

19.   Confidence Intervals for Difference of Two Means: Paired Samples

20.   Bootstrap Confidence Interval for the Difference of Two Means: Paired Samples

21.   Confidence Intervals Involving Variation

22.   Hypotheses Testing Concepts

23.   Testing of Hypotheses about Proportions

24.   Other Test of Hypotheses

25.   Contingency Tables and the Chi-Square

26.   Sample Surveys

27.   Scatterplots and Correlation

28.   Simple Linear Regression

29.   Regression Wisdom

30.   Inference for Simple Linear Regression

31.   Advanced Simple Regression: Logistic, Weibull and Lognormal

32.   Probability and System Reliability

33.   Binomial, Geometric and Poisson Distribution

34.   Maximum Likelihood Estimation

35.   Bayesian Statistics

36.   Multiple Linear Regression

37.   ANOVA for Single Factor Experiments

38.   ANOVA for Multifactor Experiments

39.   Nonparametric Statistics

Enrichment Topics

In addition, to lectures on the course topics above, there will be some enrichment lectures motivated by students’ interests. In the past, these topics have included:

 

1.       Repairable systems

2.       Reliability growth

3.       Non-Homogeneous Poisson Process (NHPP)

4.       Control charts

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*Some of these topics are touched only briefly