Probability & Statistics syllabus

Algebra | Analysis | Applied & PDE | Prob & Stat | Scientific Computation | Topology

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	Graduate studies
	Description
	Requirements
	Ph.D requirements
	Preliminary exams
	Qualifying exams

Topics

1. Random variables
   1. expectation
   2. variance
   3. covariance
2. Univariate distributions, multivariate Normal
3. Law of Large Numbers (weak, strong)
4. Central Limit Theorem
5. Hypothesis Testing
   1. Neyman-Pearson Lemma
   2. Likelihood Ratio Tests and Asymptotic Theory
6. Estimation
1. Maximum Likelihood, Method of Moments
2. Fisher Information
3. Asymptotic distribution theory for maximum likelihood estimators
4. Sufficient Statistics
7. Linear Regression
   1. Least Squares Parameter Estimation
   2. Test statistics with Normal, uncorrelated errors
8. Finite Markov chains
   1. irreducibility, aperiodicity
   2. ergodicity, stationary distribution

References

[1] Statistical Inference, by Casella and Berger, Chapters 1-5, 6.1-6.2, 7, 8, 12.1, 12.2
[2] Introduction to Mathematical Statistics by Hogg and Craig, Chapters 1-5, 6.1- 6.2, 7, 10, 12
[3] Introduction to Probability Models by Ross, Chapter 4.

Mathematics Department Tulane University 6823 St. Charles Ave New Orleans, LA 70118 phone: (504) 865-5727 fax: (504) 865-5063

Last Updated: July 19, 2005