Biostat 601 PROBABILITY AND DISTRIBUTION THEORY Fall 2018 (4 Credits) When and Where: Meeting Time: T/Th 1:00pm - 3:00pm, Meeting Place: M1755 SPH I. Fall study break: Oct 15-16th Thanksgiving: Nov 22nd. Last class on Dec 6th. Instructor: Lu Wang M4132 SPH II Phone: 647-6935 E-mail:
[email protected] Office hours: 12:00 - 1:00 pm Tue. Location: M4132 SPH II GSI: Yuming Sun E-mail:
[email protected] Office hours: One hour TBD Mondays and One hour TBD Wednesdays. Location: TBD Textbooks: • Statistical Inference, 2nd Edition, by G. Casella and R. L. Berger, Duxbury: Thomson Learning Inc (2002). (Required) • A First Course in Probability, 6th Edition, by S. Ross, Prentice Hall (2002). Prerequisites: Three terms of calculus. Lectures: The lectures will cover the first five chapters in Casella and Berger, though the material in each chapter may be expanded or tailored. Homework: Handout on Thursdays; due following Thursday. No late homework is accepted. You are encouraged to discuss homework problems with fellow students, but your final product should be based on your own understanding. Copying other’s work is not acceptable. 1
Exams: Midterm: Thursday, October 19 Final Exam: Wednesday, December 19, 1:30 pm - 3:30 pm Grading: Homework: 30%; Midterm: 30%; Final exam: 40%. Academic Integrity: The faculty of the School of Public Health believes that the conduct of a student registered or taking courses in the School should be consistent with that of a professional person. Courtesy, honesty and respect should be shown by students toward faculty members, guest lecturers, administrative support staff and fellow students. Similarly, students should expect faculty to treat them fairly, showing respect for their ideas and opinions and striving to help them achieve maximum benefits from their experience in the School. Student academic misconduct refers to behavior that may include plagiarism, cheating, fabrication, falsification of records or official documents, intentional misuse of equipment or materials (including library materials), and aiding and abetting the perpetration of such acts. The preparation of reports, papers, and examinations, assigned on an individual basis, must represent each student’s own effort. Reference sources should be indicated clearly. The use of assistance from other students or aids of any kind during a written examination, except when the use of aids such as electronic devices, books or notes has been approved by an instructor, is a violation of the standard of academic conduct.
Outline of Lectures: Chapter 1 • Brief review of combinatorial analysis • Sample space, events, and set operation • Axioms of probability • Properties of probability function • Probabilities in finite sample space • Conditional probability and independence • Random variables 2
• Distribution, density, expectation, and variance Chapter 2 • Functions of a random variable • Moments and moment generating functions • Dominated convergence theorem, interchanging integration and differentiation Chapter 3 • Examples of discrete distributions • Examples of continuous distributions Chapter 4 • Joint distribution functions • Conditional distributions and independence • Expectation, covariance, and correlation coefficient • Important inequalities • Distributions of Functions of Random Variables Chapter 5 • Distributions of some sample statistics • Order statistics • Modes of convergence: almost sure, in probability, in distribution • Classical limiting theorems: weak law, strong law, central limit theorems, and some other important theorems • Delta method
Competencies covered in this course:
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• Describe the roles biostatistics serves in the discipline of public health. (partially covered) • Describe basic concepts of probability, random variation and commonly used statistical probability distributions. (fully covered) • Describe preferred methodological alternatives to commonly used statistical methods when assumptions are not met. (partially covered) • Distinguish among the different measurement scales and the implications for selection of statistical methods to be used based on these distinctions. (partially covered) • Apply descriptive techniques commonly used to summarize public health data. (partially covered) • Apply common statistical methods for inference. (partially covered) • Apply descriptive and inferential methodologies according to the type of study design for answering a particular research question. (partially covered) • Interpret results of statistical analyses found in public health studies. (partially covered) • Develop written and oral presentations based on statistical analyses for both public health professionals and educated lay audiences. (partially covered) • Apply the basic terminology and definitions of epidemiology. (partially covered) • Calculate basic epidemiology measures. (partially covered) • Draw appropriate inferences from epidemiologic data. (partially covered) • Apply evidence-based principles and the scientific knowledge base to critical evaluation and decision-making in public health. (partially covered)
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