COMPREHENSIVE EXAMINATION
SYLLABUS
Parts -IA, IB
Students may review the textbooks that were used in the Probability and Mathematical Statistics sequence (MAT-451, 452 & 453).
The exams are given in two parts and must be taken on the same day, on a Saturday 9:00 A.M. - 4:00 P.M., in October and/or April/May.
Students who intend to take the exams in a given quarter should notify the program director, in writing, early in the quarter.
Part-IA:
This is a three-hour closed-book exam. It covers analytical and theoretical concepts of probability and statistical inference [items 1-5, and major theorems in items 6 and 7 of the following list of topics]. Normally, this exam is given between 9:00 A.M.-12:00 noon.
Part-IB:
This is a three-hour open-book exam. It covers topics of statistical inference described in items 6-11 of the following list of topics. Notes, books, tables, and calculators may be used. This exam is given between 1:00-4:00 P.M. the same day as part I-A.
1. Elements of probability.
2. Probability distributions: their moments, moment-generating functions, functions of random variables, and transformation of variables.
3. Discrete Probability models: Bernoulli, Binomial, Poisson, Geometric, negative binomial, hyper-geometric, multinomial distributions.
4. Continuous Probability Models: Uniform, exponential, Gamma, c2, Beta, Normal, Student-t, and Fisher’s F-distributions.
5. Sampling distributions of means, variances, proportions. Laws of large numbers, the Central Limit Theorem.
6. Estimation: Properties, methods, point and interval estimation.
7. Hypothesis testing: Neyman-Pearson lemma, most powerful tests, simple and composite hypothesis tests of means, variances and proportions.
8. The Analysis of Variance (one-way ANOVA).
9. Linear Regression and the least-squares method.
10. Nonparametric methods of inference (Wilcoxon-Mann-Whitney, Sign, Kruskell-Wallis, Friedman, Runs tests, and Spearman’s Correlation.)
11. c2 -tests of Goodness of Fit, Independence and Homogeneity.