MA 212M: Mathematical Statistics
Course Syllabus
Probability: Probability spaces, random variables and random vectors, functions of random vectors, univariate and multivariate distributions, mathematical expectations, moment generating functions, convergence in probability and in distribution and related results; Sampling distributions.
Statistics: Point estimation - estimators, sufficiency, completeness, minimum variance unbiased estimation, maximum likelihood estimation, method of moments, Cramer-Rao inequality, consistency; Interval estimation; Testing of hypotheses - tests and critical regions, Neymann-Pearson lemma, uniformly most powerful tests, likelihood ratio tests; Correlation and linear regression.
Text Books
- Introduction to Mathematical Statistics by R. V. Hogg, J. W. McKean and A. Craig.
- Introduction to Probability Models by S. M. Ross.
Reference Books
- An Introduction to Probability and Statistics by V. K. Rohatgi and A. K. Md. E. Saleh.
Evaluation
Weights in different examinations are as follows:
- Quiz I: 15% (February 06 during class)
- Mid-semester examination: 30% (March 07 from 9 am to 11 am)
- Quiz II: 15% (April 10 during class)
- End-semester examination: 40% (May 09 from 9 am to 12 am)
For each examination, linear scaling will be used (if needed).
An F grade will be awarded if you obtain less than 20% of total marks after the end semester examination.
Course Materials
Lecture Slides
- Topic 00: Introduction
- Topic 01: Probability
- Topic 02: Random Variable
- Topic 03: Random Vector
- Topic 04: Modes of Convergence
- Topic 05: Sampling Distributions
- Topic 06: Point Estimation
- Topic 07: Interval Estimation
- Topic 08: Testing of Hypotheses
- Topic 09: Simple Linear Regression
- Topic 10: Multiple Linear Regression
- Topic 11: Logistic and Poisson Regression