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MATH 346 : Probability and Statistics II

Credits: 3

Course Description: This is a statistics course for students with a firm mastery of calculus, emphasizing the mathematical and conceptual bases of statistics, with a view to understanding the proper application of standard methods. The course includes thorough treatments of the Central Limit Theorem, the theory of estimation, hypothesis testing, and regression.

Pre-Requisites: MATH 345.

Sample Materials

  1. Probability review: random varaibles, special distributions, expectation, variance, standard deviations, moments;
  2. Central Limit Theorem, statistics vocabulary: population, sample, statistics: sample mean, sample variance, sample moments;
  3. Parameter estimation: maximum likelihood estimate, method of moments estimate;
  4. Parameter estimation properties: bias, efficiency, sufficiency;
  5. Confidence intervals;
  6. Introduction to hypothesis testing: hypotheses, type I and II errors, power, significance level;
  7. Generalized likelihood ration, Neyman-Pearson lemma;
  8. Statistical inference for normally distributed data: t and F- tests;
  9. Two-population sample problems: paired and two-population t-tests, two-population tests for binomial data;
  10. Goodness-of-fit tests, contingency tables, chi-square test, exact test;
  11. Regression analysis: linear model, least square estimators and their properties;
  12. Multiple linear regression, correlation coefficient;
  13. Nonparametric tests: sign test, Wilcoxon test;
  14. ANOVA: one-way analysis of variance, Tukey’s method.

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