Mathematics 206

Course Outline

LENGTH OF COURSE: One semester (14 weeks)
 
CLASSROOM HOURS PER WEEK: 4 hours of lectures
 
NUMBER OF UNITS OF CREDIT: 3 credit hours
    Simon Fraser University - 3 credits
    University of British Columbia - 3 credits
    University of Victoria - 1.5 units
PRESENT TRANSFERABILITY
    Simon Fraser University - Statistics 270 (3)
    University of British Columbia - Statistics 2nd (3). Precludes credit for UBC statistics 241 and 251
    University of Victoria - 1.5 unassigned second-year Mathematics units
PREREQUISITE
    Columbia College Mathematics 113 and 114 or the equivalent. (With permission of the instructor, students may take Mathematics 114 concurrently.)
AUDIENCE: This course is designed for serious students of mathematics, science or computer science.
 
CALENDAR DESCRIPTION
A calculus-based introduction to probability and mathematical statistics, including sampling theory, random variables, the special distributions of statistical theory, and hypothesis testing.
 
COURSE OUTLINE
1) Probability (3 weeks)
Sample spaces, the probability function, discrete and continuous probability functions, conditional probability, independence, independent trials, combinatorics, combinatorial probability, binomial and hypergeometric distributions.
 
2) Random Variables (5 weeks)
Densities and distributions, joint densities, independent random variables, transformations of random variables, order statistics, conditional densities, expected values and their properties, variance, covariance and correlation, higher moments, moment-generating functions, Chebyshev's inequality.
 
3) Special Distributions (3 weeks)
Poisson distribution, normal distribution, central limit theorem, geometric distribution, negative binomial distribution, exponential and gamma distributions.
 
4) Hypothesis Testing (2 weeks)
The decision rule, Type I and Type II errors, generalized likelihood ratio.
 
TEXTBOOK: William Mendenhall, Dennis D. Wackerly, Richard L. Scheaffer,
    Mathematical Statistics with Applications, Fifth Edition, Duxbury Press, Wadsworth Publishing Company, 1996
    Sections of the textbook relevant to the above topics: Chapter 2 to Chapter 5, Chapter 10
COURSE EVALUATION
    Quizzes and/or Assignments 10%
    Three One-Hour Tests 40%
    Comprehensive Final Exam 50%
INSTRUCTORS
    Kim Peu Chew, B.Sc.(Nanyang), M.A., Ph.D (British Columbia)
    Sam Ekambaram, B.Sc. (Madras), Ph.D. (Simon Fraser)
    Peter Hurthig, B.Sc., M.Sc., (British Columbia)
    David Medalen, B.A.(St. Olaf), M.Sc., (British Columbia)