Material for Preliminary Exam B --- Statistics Section
The following list gives topics on which the Preliminary Examination B in Statistics will be based. STATS 5312 and 5313 (MATH 5312-13) cover many, but not necessarily all, of these topics. Students (even those who have taken STATS 5312-13) are advised to prepare
for the examination using many resources, including (but not limited to) the books suggested below.
1. Introduction to Probability
Combination and permutation
Properties of probability
Independent events
Conditional probability
Bayesâ€™ rule
2. Distributions
Continuous distributions
Discrete distributions
Joint distributions
Properties of distributions
Moment generating functions
3. Function of random variable and limiting distributions
The CDF technique
Transformation methods
Moment generating function methods
Central Limit Theorem
Sampling distributions.
4. Point estimation
Methods of estimation
Maximum likelihood estimators
Properties of estimators-bias, consistency, efficiency, etc.
Uniformly minimum variance unbiased estimators
Distributions of estimators
5. Interval estimation
Pivotal quantity method
Confidence interval for the mean(s)
Confidence interval for the variance(s)
Large sample confidence intervals
6. Testing statistical hypotheses
Simple and composite hypotheses
Uniformly most powerful test
Tests for normal distributions
Goodness-of-fit test
Contingency tables
Suggested Reading
1. Hogg, Robert, Allen Craig and Joseph McKean (2004). Introduction to Mathematical Statistics, 6^{th} Edition, Macmillan Company.
2. Bain, Lee J. and Max Engelhardt (1991). Introduction to Probability and Mathematical Statistics, 2nd Edition, Duxbury.