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

• Bayes’ 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.