# Mathematical Statistics

Rutgers MATH 481, Fall 2020.
Mathematical Statistics

Lecture 0: General overview
Lecture 1: Probability review/overview, part 1
Lecture 2: Probability review/overview, part 2. Uniform, gamma and normal distributions
Lecture 3: Probability review/overview, part 3. Central limit theorem
Lecture 4: Sampling distributions and a first look at estimation of means
Lecture 5: Interval estimation intro and confidence intervals for the mean
Lecture 6, part 1: Sample variance and the chi square distribution
Lecture 6, part 2: The what and why of the chi square distribution
Lecture 7: Confidence intervals for population variance
Lecture 8: Normal approximation for chi square for large n
Lecture 8.5: Doing better than just the central limit theorem for approximating chi square for medium size n
Lecture 9: The t-distribution and sampling from normal populations with unknown variance
Lecture 10: The f-distribution
Supplemental Lecture 10.1: The f-distribution: Working with multiple sample variances from a single population
Supplemental Lecture 10.2: The f-distribution: working with ratios of variances
Supplemental Lecture 10.3: The f-distribution: confidence intervals for ratios of variances
Lecture 11, part 1: Unbiased estimators
Lecture 11, part 2: Efficiency of estimators
Lecture 12: Consistent estimators
Lecture 13: Sufficient estimators
Lecture 14.1: How do we find estimators?
Lecture 14.2: The method of moments
Lecture 14.3: Detour: Jensen's inequality
Lecture 15: Maximum likelihood estimators
Lecture 16: Bayesian estimation of parameters
Lecture 17: Introduction to hypothesis testing
Lecture 18: Hypothesis testing: basic examples
Lecture 19: Hypothesis testing: more examples
Lecture 20: Most powerful regions and the Neyman-Pearson Lemma
Lecture 20.1: Supplimentary examples on simple and compound hypotheses
Lecture 21, part 1: The power function of a test concerning composite hypotheses
Lecture 21, part 2: Likelihood ratio tests
Lecture 21, part 3: Introduction to using likelihood ratio tests
Lecture 22: Likelihood ratio test example featuring the t-distribution
Lecture 23, part 1: Regression Analysis: Basic concepts
Lecture 23, part 2: Regression Analysis: Normal regression analysis
Lecture 23, part 3: Regression Analysis: Normal correlation analysis