Statistics and Probability Preliminary Exam Syllabus
Texts:
- J. E. Freund, Mathematical Statistics, 5th Edition
- B. W. Lundgren, Statistical Theory, 3rd Edition
For understanding the concept of sufficiency
and its relationship to the reduction of data
and to the reduction of variance.
- S. M. Ross, Introduction to Probability Models,
6th Edition: Chapters 1 through 6, except sections 4.9 and 4.10.
- Basic Probability
- Conditional probability and independence
- Random variables, probability mass and density functions,
conditions defining the binominal, Poisson, normal, and
exponential distributions of functions of random variables
- Expectation and conditional expectation
- Limit Theorems
- Law of large numbers
- Central limit theorem
- Markov Chains (Effective with the January 2000 prelim)
- Discrete and continuous time Markov Chains
- Poisson process
- Estimation
- Point estimation, unbiasedness, consistency, efficiency, maximum
likelihood estimation, Bayes estimators
- Confidence intervals, pivotal method, general method,
simultaneous confidence regions
- Sufficiency
- Definition and factorization theorem
- Reduction of data
- Reduction of variance
- Hypothesis Testing
- Neyman-Pearson lemma
- Composite hypothesis, likelihood ratio tests, -2log[[Lambda]]
- Tests of independence and goodness of fit
- Regression and Analysis of Variance
- Estimation, method of least squares
- Hypothesis testing
- Nonparametric Statistics
- Sign tests
- Wilcoxon rank tests
This page was last updated on August 20, 2002 by
Anne Dougherty.