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

Topics:

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


			Department of Mathematics University of Massachusetts Boston Phone: 617-287-6460; Fax: 617-287-6433 Information: math-info@math.umb.edu