712—Mathematical Statistics I (3) (Prereq: Advanced calculus or consent of instructor) Sample spaces, probability and conditional probability, independence, random variables, expectation, distribution theory, sampling distributions, laws of large numbers and asymptotic theory, order statistics, and estimation.
Usually Offered: Fall Semesters
Purpose: To acquaint beginning graduate students in statistics and other disciplines with the concepts of probability and the mathematical development of statistics. To provide a foundation for further study in probability theory and statistical theory at both the master's and doctoral levels.
Current Textbook: Statistical Inference, 2nd Edn., by G. Casella & R.L. Berger, Duxbury, 2002.
|Elements of Probability: Sample spaces, events (Borel sets), axioms and laws of probability, independence, conditional probability, Bayes Theorem, discrete and continuous random variables and vectors, distribution functions, densities||3.5 weeks|
|Expectation & Functions of Random Variables: functions of random variables, moments, generating and characteristic functions||2 weeks|
|Specific Parametric Distributions-Univariate: Binomial, Poisson, Hypergeometric, geometric,negative binomial, exponential, gamma, normal and related families, exponential families||2 weeks|
|Distribution Theory: Joint distributions, conditional distributions, independence of random variables, probability inequalities for random variables (Chebyshev, Jensen), Multivariate distributions: trinomial, multinomial, bivariate normal||2 weeks|
|Sampling Distributions & Convergence Concepts: Random samples, central limit theorem, laws of large numbers, Slutzky's theorem, Normal models, order statistics||2.5 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.