511—Probability [=MATH 511] (3) (Prereq: MATH 241 with a grade of C or higher) Probability and independence; discrete and continuous random variables; joint, marginal, and conditional densities; moment generating functions; laws of large numbers; binomial, Poisson, gamma, univariate and bivariate normal distributions.
Usually Offered: Fall, Spring, and Summer I semesters.
Purpose: To provide a strong foundation in basic probability for understanding the concepts and modelling of random phenomena, and to prepare students for study of the mathematical development of statistical methodology.
Current Textbook: Mathematical Statistics with Applications (7th Ed.), D. Wackerly, W. Mendenhall and R. Sheaffer, Duxbury, 2008.
Instructor should contact the Undergraduate Director in Department of Statistics prior to changing the text.
|Probability axioms, sample spaces, events, counting, laws of probability, conditional probability, independence, Bayes' theorem||3 weeks|
|Discrete distributions, random variables, mathematical expectation, binomial, geometric, negative binomial, hypergeometric, and Poisson distributions, moment-generating functions||3.5 weeks|
|Continuous distributions, random variables, mathematical expectation, uniform, gamma, normal, exponential, beta, and other distributions, inequalities, mixture distributions||3.5 weeks|
|Bivariate distributions, marginal and conditional distributions, covariance and correlation, conditional expectation||4 weeks|
The above textbook and course outline should correspond to the most recent offering of the course by the Statistics Department. Please check the current course homepage or with the instructor for the course regulations, expectations, and operating procedures.